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

Given that

Sn = 5n2 + 3n


Put n = 1


S1= T1= 5 + 3 = 8


Put n = 2


S2= 5(2)2 + 3 + 2 = 26


T2= S2 – S1 = 26 – 8 = 18


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


T3= S3 – S2 = 54 – 26


= 28


Therefore, first term, a = 8 and common difference = 18 – 8 = 10


Tm = a + (m – 1) d


168 = 8 + (m – 1) 10


168 = 8 + 10m – 10


170 = 10m


m = 17


T20 = 8 + (20 – 1) 10


= 8 + 19 * 10 = 198


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