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.

Answer»

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 x 10 = 198



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