SOLUTION: The sum of 8th terms of an AP is 160 while the sum of 20 terms is 880. Find (a) the 43rd term (b) the sum of 12 terms.

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Question 1134390: The sum of 8th terms of an AP is 160 while the sum of 20 terms is 880. Find (a) the 43rd term (b) the sum of 12 terms.
Answer by greenestamps(13200) About Me  (Show Source):
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Let a and d be the first term and common difference, respectively. Then

the 8th term is a+7d
the 20th term is a+19d

The sum of the first 8 terms is
(a)+(a+d)+(a+2d)+...+(a+7d) = 8a+28d

The sum of the first 20 terms is
(a)+(a+d)+(a+2d)+...+(a+19d) = 20a+190d

So

8a%2B28d+=+160
20a%2B190d+=+880

40a%2B140d+=+800
40a%2B380d+=+1760
240d+=+960
d+=+4
8a%2B112+=+160
8a+=+48
a+=+6

The first term is 6 and the common difference is 4.

The 43rd term is a+42d = 6+42(4) = 6+168 = 174

The sum of the first 12 terms is
(a)+(a+d)+(a+2d)+...+(a+11d) = 12a+66d = 12(6)+66(4) = 72+264 = 336