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 Sn = 5n2 + 3n,
On putting n = 1, we get the first term(a), S1 = a = 5(1)2 + 3(1) = 8
On putting n = 2 gives S2 = a + a + d = 5(2)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.