Question

Which of the following sequences is an A.P. with commondifference 3

(a) a= 2n^2 + 3n, n € N
(b) a, = 3n^2 + 5, n € N
(c) a, = 3n^2 + 1, n € N
(d) a, = 2n^2 + 3, n € N​

Answer 1

Answer:

Given that S

n

=2n

2

+3n

S

1

=2(1)

2

+3(1)=2+3=5

So, sum of the first term of A.P. is 5

⟹ first term a=5

S

2

=2(2)

2

+3(2)=8+6=14

So, sum of the first two terms of A.P. is 14

⟹ first term +second term =14

⟹5+a

2

=14

⟹a

2

=9

Therefore, common difference = second term - first term

⟹d=14−5=9

Therefore, t

20

=a+(20−1)d

⟹t

20

=5+(19)9

⟹t

20

=5+171=176