Question

4. In an AP. first term is 1 and last term is 11. If the sum of n terms is 36, the value of n will be:
(a) 10
(6) 7
(c) 6
(d)5​

Answer 1

and the sum of its terms is 36

Let, the number of terms be n and common difference be d.

We know, the formula of n

th

term of an A.P is

t

n

=a+(n−1)d

And, the formula of term n− terms of an A.P is,

S

n

=

2

n

[2a+(n−1)d]

By the question

t

n

→1+(n−1)d=11

⇒ d=

n−1

10

...(i)

S

n

→

2

n

[2.1+(n−1)d]=36

⇒ 2+(n−1)d=

n

72

⇒ d=

n(n−1)

72−2n

....(ii)

Comparing (i) and (ii) we get,

n(n−1)

10

=

n(n−1)

72−2n

⇒ 10n=72−2n

⇒ 12n=72

⇒ n=6

Hence, the number of terms is 6