And Saul, and Jonathan his son, and the people that were present with them, stayed in Gibeah of Benjamin: but the Philistines encamped in Michmash. Jump to: Barnes • Benson • BI • Cambridge • Clarke • Darby • Ellicott • Expositor's • Exp Dct • Gaebelein • GSB • Gill • Gray • Haydock • Hastings • Homiletics • JFB • KD • KJT • Lange • MacLaren • MHC • MHCW • Parker • Poole • Pulpit • Sermon • SCO • TTB • WES • TSK (16) Gibeah of Benjamin.—Saul and his son, uniting their sadly diminished forces, entrench themselves at Geba, in a strong position at the end of a pass, whence they could watch the movements of the Philistines. Their small number forbade any idea of an attack on the enemy. The English translators wrongly here substitute “Gibeah of Benjamin” for “Geba of Benjamin,” probably led astray by the mention of Gibeah in the preceding verse. 13:15-23 See how politic the Philistines were when they had power; they not only prevented the people of Israel from making weapons of war, but obliged them to depend upon their enemies, even for instruments of husbandry. How impolitic Saul was, who did not, in the beginning of his reign, set himself to redress this. Want of true sense always accompanies want of grace. Sins which appear to us very little, have dangerous consequences. Miserable is a guilty, defenceless nation; much more those who are destitute of the whole armour of God.Samuel arose - Saul could not return to his own station at Michmash, seeing it was occupied by the Philistines; so, perhaps by Samuel's advice (since, according to the text, he preceded him there), he effected a junction with Jonathan at Gibeah. Some would read 'Saul' instead of 'Samuel.' 15, 16. Samuel … gat him … unto Gibeah … and Saul, and Jonathan his son, and the people that were present with them, abode in Gibeah—Saul removed his camp thither, either in the hope that, it being his native town, he would gain an increase of followers or that he might enjoy the counsels and influence of the prophet. No text from Poole on this verse. And Saul, and Jonathan his son,. Who were now joined to their men, on Saul's coming to Gibeah: and the people that were present with them; the six hundred men before numbered: abode in Gibeah of Benjamin; being perhaps a strong fortified place, not choosing to go forth to meet the army of the Philistines, so vastly superior to them: but the Philistines encamped at Michmash; the old quarters of Saul before he went to Gilgal, 1 Samuel 13:2. And Saul, and Jonathan his son, and the people that were present with them, abode in Gibeah of Benjamin: but the Philistines encamped in Michmash.16. in Gibeah of Benjamin] Heb. in Geba of Benjamin. The positions of 1 Samuel 13:2-3 are now reversed, the Philistines occupying Michmash on the northern side of the valley, Saul and Jonathan holding Geba on the southern side.Verse 16. - In Gibeah of Benjamin. This is an arbitrary change of the A.V. (in company with the Septuagint and Vulgate) for Geba, which is the word in the Hebrew text. Our translators no doubt considered that as Gibeah of Benjamin occurs in the previous verse, this must be the same place. But our greater knowledge of the geography of the Holy Land enables us to say that Geba is right; for, as we have seen, it was at one end of the defile, at the other end of which was Michmash; and here alone could the small army of Saul have any chance of defending itself against the vast host of the Philistines. However much we may blame Saul's disobedience, he was a skilful soldier and a brave man, and his going with his little band to the end of the pass to make a last desperate stand was an act worthy of a king. The offering of the sacrifice was hardly finished when Samuel came and said to Saul, as he came to meet him and salute him, 'What hast thou done?' Saul replied, 'When I saw that the people were scattered away from me, and thou camest not at the time appointed, and the Philistines were assembled at Michmash, I thought the Philistines will come down to me to Gilgal now (to attack me), before I have entreated the face of Jehovah; and I overcame myself, and offered the burnt-offering.' יי פּני חלּה: see Exodus 32:11.1 Samuel 13:16 Interlinear
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- Multitouch 1 16 13 18 Esv
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To find a missing number in a Sequence, first we must have a Rule
Sequence
A Sequence is a set of things (usually numbers) that are in order.
Each number in the sequence is called a term (or sometimes 'element' or 'member'), read Sequences and Series for a more in-depth discussion.
Finding Missing Numbers
- 13(see note 1) 27⁄ 64 ″20 29⁄ 64 28 12,24,27 12 ¾″ 9⁄ 16″ 0.5625 9⁄ 16″ 12 31⁄ 64″ 18 33⁄ 64″ 24 27 5⁄ 8″ 0.625 5⁄ 8″ 11 17⁄ 32″ 18 37⁄ 64″ 24 12,27 11⁄ 16″ 0.68753 11⁄ 16 24 ¾″ 0.75 10 21⁄ 32″ 16 20 12,27 1 1⁄ 8″ 7⁄ 8″ 0.875 9 49⁄ 64″ 14 20 12,18,27 1 5⁄ 16″ 1″ 1 8 7⁄ 8.
- 16 Gauge vs 18 Gauge Stainless Steel Sink. If you see labeling like 18/10 or also known as 304 means the percentage of chromium and nickel in the steel. The 16 gauge is better than the 18 gauge because of the lower the number, the thicker the kitchen sink. 16 gauge is quieter than the 18 gauge due to its thickness.
To find a missing number, first find a Rule behind the Sequence.
Sometimes we can just look at the numbers and see a pattern:
Example: 1, 4, 9, 16, ?
Answer: they are Squares (12=1, 22=4, 32=9, 42=16, .)
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Rule: xn = n2 Geometry dash subzero full version.
Sequence: 1, 4, 9, 16, 25, 36, 49, .
Did you see how we wrote that rule using 'x' and 'n' ?
xn means 'term number n', so term 3 is written x3
And we can calculate term 3 using:
x3 = 32 = 9
We can use a Rule to find any term. For example, the 25th term can be found by 'plugging in' 25 wherever n is. Baixaki winrar gratis em portugues.
x25 = 252 = 625
How about another example:
Example: 3, 5, 8, 13, 21, ?
After 3 and 5 all the rest are the sum of the two numbers before,
That is 3 + 5 = 8, 5 + 8 = 13 etc, which is part of the Fibonacci Sequence:
3, 5, 8, 13, 21, 34, 55, 89, .
Which has this Rule:
Rule: xn = xn-1 + xn-2
Now what does xn-1 mean? It means 'the previous term' as term number n-1 is 1 less than term number n.
And xn-2 means the term before that one.
Let's try that Rule for the 6th term:
x6 = x6-1 + x6-2
x6 = x5 + x4
So term 6 equals term 5 plus term 4. We already know term 5 is 21 and term 4 is 13, so:
x6 = 21 + 13 = 34
Many Rules
One of the troubles with finding 'the next number' in a sequence is that mathematics is so powerful we can find more than one Rule that works.
What is the next number in the sequence 1, 2, 4, 7, ?
Here are three solutions (there can be more!):
Solution 1: Add 1, then add 2, 3, 4, .
So, 1+1=2, 2+2=4, 4+3=7, 7+4=11, etc.
Rule: xn = n(n-1)/2 + 1 Is there pivot stick animator for mac.
Sequence: 1, 2, 4, 7, 11, 16, 22, .
(That rule looks a bit complicated, but it works)
Solution 2: After 1 and 2, add the two previous numbers, plus 1:
Rule: xn = xn-1 + xn-2 + 1
Sequence: 1, 2, 4, 7, 12, 20, 33, .
Solution 3: After 1, 2 and 4, add the three previous numbers Lightwave 3d 2018 0 2 – 3d animation software pdf.
Rule: xn = xn-1 + xn-2 + xn-3
Sequence: 1, 2, 4, 7, 13, 24, 44, .
So, we have three perfectly reasonable solutions, and they create totally different sequences.
Which is right? They are all right.
And there are other solutions .
. it may be a list of the winners' numbers . so the next number could be . anything! |
Simplest Rule
When in doubt choose the simplest rule that makes sense, but also mention that there are other solutions.
Finding Differences
Sometimes it helps to find the differences between each pair of numbers . this can often reveal an underlying pattern.
Here is a simple case:
The differences are always 2, so we can guess that '2n' is part of the answer.
Let us try 2n: Itext pro 1 2 5 – ocr tool windows 10.
The last row shows that we are always wrong by 5, so just add 5 and we are done:
Rule: xn = 2n + 5
OK, we could have worked out '2n+5' by just playing around with the numbers a bit, but we want a systematic way to do it, for when the sequences get more complicated.
Second Differences
In the sequence {1, 2, 4, 7, 11, 16, 22, .} we need to find the differences .
. and then find the differences of those (called second differences), like this:
The second differences in this case are 1.
With second differences we multiply by n22
In our case the difference is 1, so let us try just n22:
Multitouch 1 16 13 18 Esv
| n: | 1 | 2 | 3 | 4 | 5 |
|---|
| Terms (xn): | 1 | 2 | 4 | 7 | 11 |
|---|
| n22: | 0.5 | 2 | 4.5 | 8 | 12.5 |
|---|
| Wrong by: | 0.5 | 0 | -0.5 | -1 | -1.5 |
|---|
We are close, but seem to be drifting by 0.5, so let us try: n22 − n2
Wrong by 1 now, so let us add 1:
| n22 − n2 + 1 | 1 | 2 | 4 | 7 | 11 |
|---|
| Wrong by: | 0 | 0 | 0 | 0 | 0 |
|---|
We did it!
The formula n22 − n2 + 1 can be simplified to n(n-1)/2 + 1
So by 'trial-and-error' we discovered a rule that works:
Rule: xn = n(n-1)/2 + 1
Sequence: 1, 2, 4, 7, 11, 16, 22, 29, 37, .
Other Types of Sequences
Read Sequences and Series to learn about:
And there are also:
And many more!
In truth there are too many types of sequences to mention here, but if there is a special one you would like me to add just let me know.
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