Question

The 4th and 10th terms of an A.P. are 13 and 25 respectively. Find its (i) first term (ii) common difference (iii) 17th term.

Answer 1

Let the first term be a and common difference d.

Given $$a + 3d = 13$$ and $$a + 9d = 25$$. 

Subtracting gives $$6d = 12$$, so $$d = 2$$. 

Then $$a = 13 - 3 \times 2 = 7$$. 

17th term: $$T_{17} = 7 + (17 - 1) \times 2 = 39$$. 

So first term = 7, common difference = 2, 17th term = 39.