# In the arithmetic sequence 60, 56, 52, 48,…, starting from the first term, how many terms are needed so that their sum is 368?

In the A.P.

First term = 60

Common difference = 56 – 60 = –4

Sum of terms =

368 =

368 =

736 = n (124 – 4n)

4n2 – 124n + 736 = 0

4n2 – 92n–32n + 736 = 0

4n(n–23) –32(n–23) = 0

(4n–32)(n–23) = 0

4n = 32 or n = 23

n = 8 or n = 23

Therefore, no. of terms can be 8 or 23

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