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Question
The sum of first n terms of an A.P is 5n2 + 3n. If its mth terms is 168, find the value of m. Also, find the 20th term of this A.P.
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Solution
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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