The sum of the 1st and 17th terms of an arithmetic sequence is 40.the sum of its 1st and 18th terms is 43.what is it's common difference.

Question

10th class,scert ,first terminal examination

 

Answer 1

the nth term of an arithmetic sequence is a_n = a₁ + (n-1)d.

 

The 16th term is a₁ + 16d and the sum of the first and 17th term is 2a₁ + 16d = 40

 

Likewise or the 18th term, the sum required is 2a₁ + 17d = 43

 

The difference of these 2 sums is clearly d = 3