The sum of first m terms of an A.P. is 4 m2 - m. If its nth term is 107, find the value of n. Also, find the 21st term of this A.P.
Sm = 4m2 – m
Put m = 1
S1 = T1 = 4 – 1 = 1
Put m = 2
S2 = 4(2)2 – 2 = 14
T2 = S2 – S1 = 14 – 3 = 11
Put m = 3
S3 = 4(3)2 – 3 = 33
T3 = S3 – S2
= 33 – 14 = 19
The first term of given A.P. is 3 and common difference, d = 11 – 3 = 8
nth term of the given A.P. is 107
107 = 3 + (n – 1)8
104 = (n – 1)8
(n – 1) = 13
n = 14
the 21st term of the given A.P., T21 = 3 + (21 – 1)8
= 3 + 160 = 163