Question

If the sum of nth term of the series can be calculated by using S= 4n²+6n. What is the first term
of the AP?​

Answer 1

We have,

S

n

=4n−n

2

Taking n=1 and we get,

S

1

=4×1−1

2

=4−1

S

1

=3

So, the sum of fristr term of an A.P. is 3.

But, sum of first term will be the first term.

So, first term a=3.

Now, taking n=2 and we get,

S

n

=4n−n

2

S

2

=4×2−2

2

S

2

=4

Then, sum of first 2 terms is 4.

Now, finding Secondterm.

Then,

According to given question,

Firstterm+Secondterm=4

3+a

2

=4

a

2

=1

Hence the A.P.is

First term a=3

Common difference

d=Secondterm-firstterm

d=1-3

=-2

The third term of

a

3

=a+2d

a

3

=3+2×(−2)

a

3

=−1

Similarly, 10

th

term

a

10

=a+9d

=3+9(−2)

=3−18

=−15

Then,

n

th

termis

a

n

=a+(n−1)d

a

n

=3+(n−1)(−2)

a

n

=3−2n+2

a

n

=5−2n

Hence, this is the answer.