SOLUTION: Find the sum of the terms of the following arithmetic progressions. -10, -7, -4,.. To 12 terms. Please solve this!

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Question 884757: Find the sum of the terms of the following arithmetic progressions.
-10, -7, -4,.. To 12 terms.
Please solve this!

Found 2 solutions by JulietG, MathTherapy:
Answer by JulietG(1812) About Me  (Show Source):
You can put this solution on YOUR website!
-10 +3 = -7
-7 + 3 = -4
-4 + 3 = -1
-1 + 3 = 2
2 + 3 = 5
5 + 3 = 8
8 + 3 = 11
11 + 3 = 14
14 + 3 = 17
17 + 3 = 20
20 + 3 = 23
23 + 3 = 26
.
Added together:
-7-4-1+2+5+8+11+14+17+20+23+26 = 114

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Find the sum of the terms of the following arithmetic progressions.
-10, -7, -4,.. To 12 terms.

S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29%29, with:
S%5Bn%5D being the sum of the 12 arithmetic terms
n being the number of terms
a%5B1%5D being the 1st term, or term 1
d being the common difference
Thus, S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29%29 becomes:
S%5Bn%5D+=+%2812%2F2%29%282%28-+10%29+%2B+%2812+-+1%293%29
S%5Bn%5D+=+6%28-+20+%2B+%2811%293%29
S%5Bn%5D+=+6%28-+20+%2B+33%29
S%5Bn%5D+=+6%2813%29
highlight_green%28highlight_green%28S%5Bn%5D+=+78%29%29
You can do the check!!
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