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(Sn) = 0.
We know sum of n terms of an A.P. is given by, Sn = 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.