Question

for an AP the 5th term is 30 and the 12th term is 100. find the sum of first 20 terms of the AP.

Answer 1

5th term is 30.

Let first term be a

common difference be d.

a+(n-1)d for any nth term.

so:

a+(5-1)d=30

a+4d=30...............(1)

12th term is 100

a+(12-1)d=100

a+11d=100.....................(2)

Subtracting (1) and (2) we get:-

4d-11d=30-100

-7d=-70

d=-70/-7

=10

a+4d=30

a+40=30

a=-10

S=n/2*[2a+(n-1)d]

=20/2*[-20+19*10]

=10*[190-20]

=10*170

=1700.

Hope it helps you.

Answer 2

Answer:

1700

Step-by-step explanation:

5th term is 30.

Let first term be a

common difference be d.

a+(n-1)d for any nth term.

so:

a+(5-1)d=30

a+4d=30...............(1)

12th term is 100

a+(12-1)d=100

a+11d=100.....................(2)

Subtracting (1) and (2) we get:-

4d-11d=30-100

-7d=-70

d=-70/-7

=10

a+4d=30

a+40=30

a=-10

S=n/2*[2a+(n-1)d]

=20/2*[-20+19*10]

=10*[190-20]

=10*170

=1700