CBSE Class 10 Maths Sample Question Paper 2019 | Q8

This 2019 CBSE class 10 Maths sample question paper 2 mark question has two alternatives. Both questions are from arithmetic progressions. The first alternative is about finding the nth term from the last term of an arithmetic progression.

Question 8A: Find the 20th term from the last term of the AP: 3, 8, 13, .... , 253

Video Explanation

Explanatory Answer | 2019 Sample Question Paper Q8 A

Given Data

a = 3, l = 253, d = 8 – 3 = 5
Where l = a + (n – 1)d

Method 1 : n^th term from the last term

The n^th term from the last = l – (n - 1)d
So, the 20^th term from last = l – (20 - 1)d
= 253 - 19 × 5
= 253 – 95 = 158

Method 2 : Calculating total number of terms

Step 1: Find the total number of terms in the AP.
l = a + (n – 1)d
253 = 3 + (n – 1)5
250 = 5(n – 1)
50 = (n – 1) or n = 51

Step 2: Compute the 20th term from the last.
The 20th term from the last will be the 32nd term.
a₃₂ = 3 + (32 – 1)5
a₃₂= 3 + 155
a₃₂ = 158