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# Question 42. 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.

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This is an arithmetic progression based question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise – 9.6
In this question we have been given that The sum of first n terms of an A.P. is 5n2 + 3n.

It is given that  its mth term is 168,

Now we have to find the value of m. Also, the 20th term of this A.P.

CBSE DHANPAT RAI PUBLICATIONS
Understanding CBSE Mathematics
Class :- 10th
Question no 42

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1. Given Sn = 5n2 + 3n,

On putting n = 1, we get the first term(a), S1 = a = 5(1)+ 3(1) = 8

On putting n = 2 gives S2 = a + a + d = 5(2)+ 3(2) = 26

=> d = 26 – 2a

=> d = 26 – 16 = 10

The mth term of the A.P., am = a + (m – 1)d = 168

=> 8 + (m – 1)10 = 168

=> (m – 1)10 = 160

=> m – 1 = 16

=> m = 17

20th term of the A.P., a20 = a + 19d

= 8 + 19(10)

= 8 + 190

= 198

Hence, the value of m is 17 and 20th term of the A.P. is 198.

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