Question

the sum of the third and seventh term of an AP is 6 and their product is 8 find the sum of the first 16 terms of the AP

Answer 1

Let the first term be a and common difference be d nth term = a+(n-1)d. Given Third Term + Seventh term = (a+2d)+(a+6d) = 6 ==> a+4d = 3

Answer 2

nth term of an AP = a + (n-1)d where

a = first term, d = common difference

3rd term = a + 2d

7th term = a + 6d

Sum = 2a + 8d = 6

=> a + 4d = 3

Product is 8

(a+2d) (a+ 6d) = 8

(3-4d+2d)(3-4d+6d)= 8

(3-2d)(3+2d)= 8

9 - 4d2 = 8

d= 1/2

a= 3-4/2 = 1

Sum of n terms of an AP= (n/2) x [2a + (n-1)d]

8 x [2a + 15d]

8 x [2 + 15/2]

76