Question

the first and the last term of an ap are 4 and 81. if the common difference is 7, how many terms are there in the ap and what is their sum?

Answer 1

Given first term a = 4, common difference d = 7, last term l = 81.

We know that sum of n terms of an AP sn = n/2(2a + (n - 1) * d)

                                                                       = n/2(2(4) + (n - 1) * 7)

                                                                       = n/2(8 + 7n - 7)

                                                                       = n/2(7n + 1)   --- (1)


We know that sum = n/2(a + l)

                                 = n/2(4 + 81)

                                 = n/2(85)    -------------- (2)



On solving (1) & (2), we get

n/2(7n + 1) = n/2(85)

7n + 1 = 85

7n = 84

n = 84/7

n = 12

Therefore there are 12 terms in the AP.

Substitute n = 12 in (2), we get

sum = n/2(a + l)

        = 12/2(4 + 81)

        = 6(85)

        = 510.


Therefore the sum = 510.


Hope this helps!