Question

The 10th term of an AP is 30 and the 15th term is 45. What is the Sum upto 10th term?

Answer 1

given that

a¹⁰ = 30 and a¹⁵ = 45

solution

a+9d = 30

and

a+14d = 45

sub. eq1 and eq2

-14d +9d = -45+30

5d = 15

d= 3

put d for a

a+9×3 = 30

a= - 27 +30

a= 3

now we have

a= 3 ,d= 3 and n= 10

Sn = n/2 {2a+(n-1)d}

S¹⁰ = 10/2 { 2×3+(10-1)×3}

S¹⁰ = 5 {6+27}

S¹⁰ = 33×5

S¹⁰ = 165