Question

the sum of first m terms of an A.P is 4m2-m

if its nth term is 107.. find the value of n.

also find its 21st term of the A.P.

Answer 1

Sn = 4m²-m

a1 = S1 = 4(1)²-(1) = 3

a2 = S2-S1 = 4(2)²-2-3 = 16-5 = 11

d = a2-a1 = 11-3 = 8

nth term is 107 (given)

Tn = 107

a1+(n-1)d = 107

3+(n-1)8 = 107

n-1 = 104/8 = 13

=> n = 14

Now,

20th term

T20 = a1+19d

= 3+19×8 = 3 + 152 = 155

Answer 2

Sn=4m^2-m
a1=s1=4*1^2-1=3
a2=11
d=8
tn=107
a1+(n-1)d=107
3+(n-1)8=107
n=14
a+20d
3+20*8
3+160
=163
T20=3+19*8
3+152
=155