Question

The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another AP whose first term is – 30 and the. common difference is 8. Find n.

Answer 1

Given that, first term of the first AP, a = 8 and that of second AP, A = - 30

and common difference of the first AP, d = 20 and that of second AP, D = 8

Given that

Sum of first n terms of first AP = Sum of first 2n terms of second AP

2a + (n - 1)d 

= 2[2 A + (2n - 1)D]16 + (n - 1)20 

= 2[2 × -30 + (2n - 1)8]16 + 20n - 20 

= 2[-60 + 16n - 8]8 + 10n - 10 

= -60 + 16n - 810n - 2 

= 16n - 686n 

= 66n 

= 11