This is an arithmetic progression based question from Chapter name- Arithmetic Progression

Chapter number- 9

Exercise – 9.6

In this question we have been given the arithmetic progression. Also we have to find out how many terms of the A.P. is 27, 24, 21. . . should be taken that their sum is zero..

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Understanding CBSE Mathematics

Class :- 10th

Question no 10(v)

Given A.P. has first term(a) = 27,

common difference(d) = 24 − 27 = −3

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(27) + (n − 1)( − 3)]/2

=> 0 = n[54 + (n − 1)(-3)]

=> 0 = n[54 − 3n + 3]

=> n[57 − 3n] = 0

=> n = 0 or 3n = 57

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

=> 3n = 57

=> n = 19

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