in an AP the sum of the first 6 terms is equal to the sum of the first 8 terms. what is the sum of the first 14 terms?

Hi Aleeza,

The sum of first 6 terms is equal to the sum of first eight terms.

=> sum of seventh and eighth term = 0

=> Seventh term is equal to the eighth term in magnitude and the progression changes its sign by the eighth term.

7th term = - 8th term

6th term = -9th term and so on.

So the sum of first 14 terms will be equal to zero.

Algebraically, this question can be solved as 4(2a + 7d) = 3(2a+5d)

8a + 28d = 6a + 15d

2a = -13d

Sum of first 14 terms = 7(2a + 13d)

Since 2a = -13d, the sum will be equal to zero.