Question

How many terms of AP
17, 15, 13,11
must be
added to get sum 72​

Answer 1

Answer:

6 or 12 numbers of terms of the given A.P. can be added to get a sum of 72.

Step-by-step explanation:

The given A.P. is 17, 15, 13, 11

a = 17

d = 17 - 15

d = -2

n = ?

s(n) = n/2 (2a + (n - 1) d) = 72 [given]

72 = n/2 (2*17 + (n - 1)*(-2))

144 = n (34 - 2n +2)

144 = 34n -2n^2 + 2n

144 = 36n - 2n^2

2*72 = 2 (18n - n^2)

72 = 18n - n^2

n^2 - 18n + 72 = 0

n^2 - 12n - 6n + 72 = 0

n (n - 12) - 6 (n - 12) = 0

Therefore, we find to values of n.

n = 12

n = 6

Hence, we conclude that either 6 or 12 no. of terms from the given A.P. (17, 15, 13, 11) can be added to get a sum of 72.

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