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.

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Understanding CBSE Mathematics

Class :- 10th

Question no 42

Given S

_{n}= 5n^{2}+ 3n,On putting n = 1, we get the first term(a), S

_{1}= a = 5(1)^{2 }+ 3(1) = 8On putting n = 2 gives S

_{2}= a + a + d = 5(2)^{2 }+ 3(2) = 26=> d = 26 – 2a

=> d = 26 – 16 = 10

The m

^{th}term of the A.P., a_{m}= 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., a

_{20}= a + 19d= 8 + 19(10)

= 8 + 190

= 198

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