Question

find the sum of n terms of that series whose n terms is (2n+3)
​

Answer 1

Given,

T

n

=3

n

−2

n

Now, ΣT

n

=Σ3

n

−Σ2

n

----------- (1)

We know sum of n terms of a G.P. is

S

n

=

r−1

a(r

n

−1)

where, a = first term of G P.

r = common ratio of the G.P.

Now, Σ3

n

=

3−1

3(3

n

−1)

[a = 3 , r = 3]

=

2

3

n+1

−3

------------- (2)

Similarly, Σ2

n

=

2−1

2(2

n

−1)

[a =2, r =2]

=2

n+1

−2 -------------- (3)

Using (2) and (3) in equation (1),

ΣT

n

=

2

3

n+1

−3

−(2

n+1

−2)

ΣT

n

=

2

3

n+1

−2

n+1

+

2

1

Answer 2

Answer:

Sum on n terms of a series whose nth term is (2n+3):

Sn=n/2(a+an)

=n/2(a+2n+3)

=(na+n²+3n)/2

=[n(a+n)+n²]/2

Hope it helps.

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