• 0
Guru

# Question 56. Let there be an A.P. with first term a and common difference d. If an denotes its nth term and Sn is the sum of first n terms, then find: (i) n and Sn, if a = 5, d = 3 and an = 50.

• 0

One of the most important and exam oriented question from Chapter name- Arithmetic Progression
Class 10th
Chapter number- 9
Exercise :- 9.6
This type of question has been asked in previous years exams.

In this question we have been given that  there be an A.P.

first term a and common difference d.

Also, If an denotes its nth term and Sn is the sum of first n terms,

then we have to find n and Sn,

Where  a = 5, d = 3 and an = 50.

CBSE DHANPAT RAI publication
CBSE Mathematics Class 10th
Question 56(i)

Share

1. Given A.P. has a = 5, d = 3 and an = 50.

By using the formula of nth term of an A.P.

an = a + (n – 1)d

So,

=> 50 = 5 + (n – 1)3

=> 3(n – 1) = 45

=> n – 1 = 15

=> n = 16

Now by using the formula of sum of n terms of an A.P.

Sn = n[a + an] / 2

So,

S16 = 16[5 + 50] / 2

= 8[55]

= 440

Hence, the value of n is 16 and sum is 440.

• 0