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 asked that how many terms of the sequence 18, 16, 14…. should be taken so that their sum is zero.

CBSE DHANPAT RAI publication

CBSE Mathematics Class 10th

Question 10(i)

Given A.P. has first term(a) = 18,

Common difference(d) = 16 – 18 = -2 and sum(S

_{n}) = 0.We know sum of n terms of an A.P. is given by, S

_{n}= n[2a + (n – 1)d] / 2.=> 0 = n[2(18) + (n – 1)(-2)]/2

=> 0 = n[36 + (-2n + 2)]/2

=> n[38 − 2n] = 0

=> n = 0 or 38 – 2n = 0

Ignoring n = 0 as number of terms cannot be 0. So we get,

=> 38 – 2n = 0

=> 2n = 38

=> n = 19

Hence, the number of terms(n) is 19.