SOLUTION: in an arithmetic series t10 is 7 times the value of t3. The sum of the first 30 terms is 2460. determine the value of t6.

Question 1161060: in an arithmetic series t10 is 7 times the value of t3. The sum of the first 30 terms is 2460. determine the value of t6.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let the first term be a(1) and the common difference be d.

(1) a(10) is 7 times a(3):

(2) The sum of the first 30 terms is 2460:

Solve the pair of equations from (1) and (2):

The common difference d is 6; use it to find a(1):

The first term is -5; the common difference is 6.

The 6th term is the first term, plus the common difference 5 times:

t(6) = -5+5(6) = -5+30 = 25

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