Question

In an

a.P if sum of its first n terms is 3n2 + 5n and its nth term is 164, find the value of k

Answer 1

S = 3n2 + 5n S1 = a1 = 3+5 = 8 S2 = a1 + a2=6+10 =16                    ⇒a2 = 8 S3 = a1 + a2+ a3  = 9 + 15 = 24        ⇒a3 = 8 ∴ AP is 8,8,8,..... Thus a =8 , d=0           Sm = 164Sum of AP = n/2 [2a + (n-1)d] 164 = m/2 [2(8) + (m-1)0] 164 = m/2[16+0] 164 = m * 16 / 2 m = 164 * 2 /16 m = 20.5
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Answer 2

hope this is correct

n=k
hence value of k is 27