Question

The 7th term of an A.P. is – 4 and its 13th term is –16. Find its (i) first term (ii) common difference (iii) nth term.

Answer 1

Let the first term be a and common difference d.

Given $$a + 6d = -4$$ and $$a + 12d = -16$$. 

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

Then $$a = -4 - 6 \times (-2) = 8$$. 

nth term: $$T_n = 8 + (n - 1) \times (-2) = 10 - 2n$$. 

So first term = 8, common difference = –2, nth term = 10 – 2n.