• 0
Guru

# Question 26. The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find the common difference.

• 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 the first and the last terms of an A.P. are 7 and 49 respectively.

Also sum of all its terms is 420

Now we have to  find the common difference

CBSE DHANPAT RAI publication
CBSE Mathematics Class 10th
Question 26

Share

1. Given A.P. has first term(a) = 7, last term(an) = 49 and sum(Sn) = 420.

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

Sn = n[a + an] / 2

So,

=> 420 = n[7 + 49]/2

=> 28n = 420

=> n = 15

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

an = a + (n – 1)d

So,

=> 49 = 7 + (15 – 1)d

=> 14d = 42

=> d = 3

Hence, the common difference of the given A.P. is 3.

• 0