Question

The Sum of first 6th team of AP is 144 and 20 term is 156. find the is 156. find the sum of n term.
please give solution please​

Answer 1

Answer:

We have the sum of first n terms of an AP,

S

n

=

2

n

[2a+(n−1)d]

Given,

36=

2

6

[2a+(6−1)d]

12=2a+5d ---------(1)

256=

2

16

[2a+(16−1)d]

32=2a+15d ---------(2)

Subtracting, (1) from (2)

32−12=2a+15d−(2a+5d)

20=10d ⟹d=2

Substituting for d in (1),

12=2a+5(2)=2(a+5)

6=a+5 ⟹a=1

∴ The sum of first 10 terms of an AP,

S

10

=

2

10

[2(1)+(10−1)2]

S

10

=5[2+18]

S

10

=100

This is the sum of the first 10 terms