Q23 of 49 Page 1

The sum of first n terms of an A.P. is 5n2 + 3n. If its mth term is 168, find the value of m. Also find the 20th term of this A.P.

Sum of first n terms = 5n2 + 3n

Putting n = 1, we get


S1 = 5(1)2 + 3(1) = 8


Putting n = 2, we get


Sum of first 2 terms = S2 = 5(2)2 + 3(2) = 26


⸫ The second term = 26 – 8 = 18


Putting n = 3, we get


S3 = 5(3)2 + 3(3) = 54


⸫ The third term = 54 – 26 = 28


⸫ First term = a = 8


⸫ Common difference = d = 10


The formula for nth term of an A.P. is given by,


an = a + (n – 1) d


mth term = am = a + (m – 1) d = 168


⇒ 8 + (m – 1) 10 = 168


⇒ 8 + 10m – 10 = 168


⇒ 10m = 170


⸫ m = 17


⸫ a20 = 8 + (20 – 1) 10


= 198


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