Question

The third and the 7th terms of an Ap are 13 and 33 respectively.find the nth term of the Ap

Answer 1

so let the first term of the AP be a and the common difference be d

using n th term =  a + (n - 1)d 
so given 

a + 2d = 13  ................. i

a + 6d = 33 ....................ii 

substracting i from ii we get

4d = 20 ⇒ d = 5 

and so a + 2 x 5 = 13 ⇒ a = 3

so the nth term is = 3 + (n - 1)5 = 5n - 2

Answer 2

using n th term =  a + (n - 1)d 
you substitute andfind values