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

Step-by-step explanation:

S10 = 175 , S11 to 20 = 475

S20 = S1 to 10 + S11 to 20

S20 = 175 + 475

S20 = 650

we know that

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

If n = 10

S10 = 10 / 2 { 2a + ( n -1 ) d }

175 = 5 { 2a + 9d }

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

If n = 20

S20 = 20/2 [ 2a + ( 20-1) d ]

650 = 10 [ 2a + 19d]

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

From Equation. 1 and 2 we get

2a + 9d = 35

2a + 19d = 65

= 0 - 10d = -30

d = 3

From Equation 1

2a + 9d = 35

2a + 9(3) = 35

2a + 27 = 35

2a = 35 - 27

2a = 8

a = 8/2 = 4

a =. 4

General from of A.P is

a , a+d , a+2d , a+3d....

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

4 , 7, 10, 13 .... are in AP.

Hope it helps you