Question

find the 10th term of sequence whose sum to n terms is 6n^2+7

Answer 1

N=1
S1=13
N=2
S2=31
D=31-13=18
N=10
TN=A+(N-1)D
T10=13+(10-1)*18
13+9*18=13+162=175

Answer 2

sum of nth term is 6n² + 7
and we know that,
last term = Sn - Sn-1
= 6n ² + 7 - [ 6( n -1 )² + 7 ]
= 6n² +7 - [ 6n² + 6 - 12n + 7 ]
= 6n² + 7 - 6n² - 6 +12n - 7
= 12n - 6
last term = 12n - 6
now,
10th term = 12×10 - 6
= 120 - 6
= 114