The 2nd, 31st and the last terms of an AP are 7 and –6 respectively. Find the first term and the number of terms.

To Find: First term and number of terms.


Given: a2= , a31 = , and an =


Formula Used: an = a + (n - 1)d


(Where a=a1 is first term, a2 is second term, an is nth term and d is common difference of given AP)


By using above formula, we have


a2 = = a + d and a31 = = a + (31 - 1)d


on solving both equation, we get


a = 8 and d = –0.25


Now an = = 8 + (n - 1)( –0.25)


On solving the above equation, we get


n= 59


So the First term is equal to 8 and the number of terms is equal to 59.


2