Question

the sum of the first twelve terms of arithmetic progression [AP] is 168. if the third term is 7. find the value of the common difference and the first term ​

Answer 1

Common difference = 2

First term = 3.

Explanation:

3rd term = a1 + (3 - 1)d = 7 where a1 = first term and d = the common difference.

Sum of the first 12 terms = (12/2)[2a1 + (12-1)d] = 168

so 6(2a1 + 11d) = 168

So simplifying, we have the following system:

a1 + 2d = 7 ..................(A)

12a1 + 66d = 168

2a1 + 11d = 28.................(B) Multiplying equation A by - 2:

-2a1 - 4d =- -14 Adding this to equation B

7d = 14

d = 2

Now plug this into equation A:

a1 + 2(2) = 7

a1 = 7-4

a1 = 3.