Question

If the sum of first 10 terms of an A.P is 175 & the sum of next ten terms is 475.

Find the A.P.​

Answer 1

Answer:

The required AP is 4, 7, 10, 13, ... Step-by-step explanation: It is given that the sum of first 10 terms is 175 and the sum of the next 10 terms is 475.

Step-by-step explanation:

The required AP is 4, 7, 10, 13, ...

It is given that the sum of first 10 terms is 175 and the sum of the next 10 terms is 475.

Let the first term be a and the common difference be d.

The sum of an AP is

S_n=\frac{n}{2}[2a+(n-1)d]S

n

=

2

n

[2a+(n−1)d]

The sum of 10 terms is

S_{10}=\frac{10}{2}[2a+(10-1)d]S

10

=

2

10

[2a+(10−1)d]

175=5[2a+9d]175=5[2a+9d]

35=2a+9d35=2a+9d .... (1)

The sum of 20 terms is

S_20=\frac{20}{2}[2a+(20-1)d]S

2

0=

2

20

[2a+(20−1)d]

175+475=10[2a+19d]175+475=10[2a+19d]

65=2a+19d65=2a+19d .... (2)

On solving (1) and (2) we get

a=4, d=3a=4,d=3

The AP is

4,4+3,4+2(3)+4+3(3)+...4,4+3,4+2(3)+4+3(3)+...

4, 7, 10, 13...4,7,10,13...