This is the basic and conceptual question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise 9.6
In this question we have been given that in an A.P., the first term is 22, the common difference is –4 and the sum to n terms is 64, now we have to find number of total terms.
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Class:- 10th
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Question 19
Given A.P. has first term(a) = 22, common difference(d) = −4 and sum(Sn) = 64.
We know sum of n terms of an A.P. is given by Sn = n[2a + (n − 1)d] / 2.
=> 64 = n[2(22) + (n − 1)(−4)]/2
=> 64 = n[44 − 4n + 4]/2
=> 48n − 4n2 =128
=> 4n2 − 48n + 128 = 0
=> n2 − 12n + 32 = 0
=> n2 − 8n − 4n + 32 = 0
=> n(n − 8) − 4(n − 8) = 0
=> (n − 8)(n − 4) = 0
=> n = 8 or n = 4
Hence, the number of terms are either 4 or 8.