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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The value of m is equal to 17.
The 20th term of the A.P is equal to 198.
Given that the sum of n terms of an A.P is equal to 5n² + 3n.
S1 (sum of the 1st term) = 8 = a
S2(sum of 1st and 2nd term) = 26 = a + a + d
=> 2a + d = 26
=> d = 26 - 16
=> d = 10
Common difference of the arithmetic progression is 10 and the first term is 8.
Nth term = 8 + (n-1)×10
=> 168 = 8 + (m-1)× 10
=> m = 17
The 20th term of the arithmetic progression= 8 + (20-1)×10
= 198
= 198
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