Question

The first and last term of an ap are 1 and 11 if the sum of its terms is 36 then a = ______,d=_____,n=_____&a_n=_________

Answer 1

Let a be the 1st term, and l be the last term.

Let S_n be the sum of n terms of an AP

Given -

a = 1

l = 11

S_n = 36

The formula for the sum of n terms of an AP, when the 1st term and the last term of the AP is given, is

S_n = n/2 (a + l)

Applying this formula:

36 = n/2 (1 + 11)

=> 72 = 12n

=> n = 72/12 = 6

Given First term = 1 therefore a = 1
Last Term = 11 Therefore a_{n = 11}

6th Term is 11,
Therefore a6 = a +(6-1)d
11 = 1 + 5d
=> d = 2