SOLUTION: The sum of 8terms on AP is 160 while the sum of 20 terms is 880 find The 43rd tert The sum of 12 terms

Question 1173732: The sum of 8terms on AP is 160 while the sum of 20 terms is 880 find
The 43rd tert
The sum of 12 terms

Found 2 solutions by greenestamps, Boreal:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The sum of 8 terms is 160, so the average of the 8 terms is 160/8=20.

The average of the 8 terms is the average of the first term, a, and the 8th term, a+7d:

(1)

The sum of 20 terms is 880, so the average of the 20 terms is 880/20 = 44.

The average of the 20 terms is the average of the first term, a, and the 20th term, a+19d:

(2)

Comparing (1) and (2), we see 12d=48, so the common difference d is 4.

Then either (1) or (2) tells us that the first term is 6.

ANSWERS:

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

Sum of (first) 12 terms: 12 times the average of the first and 12th:

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Sn=(n/2)(2a+(n-1)d)
160=4(2a+7d)
2a+7d=40
and
880=10(2a+19d)
2a+19d=88
12d=48 subtracting top from bottom
d=4
that makes a=6
6/10/14/18/22/26/30/34=160
sun of 12 terms is
S12+6(12+4(11))=336
160+38+42+46=50=336
-
43rd term is a+(n-1)d=6+(42)*4
=174

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