Question

Write any three arithmetic progressions with sum of first five terms is 30.​

Answer 1

Answer:

a=2,d=2

a=4,d=1

a=0,d=3 are the APs

Answer 2

The three arithmetic progressions with sum of first five terms is 30 are as follows.

Given,

Sn = 30

n = 5

we use the formula,

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

30 = 5/2 [ 2a + (5 - 1) d ]

12 =  2a + 4d

6 = a + 2d

(i)

when a = 2, d = (6 - a)/2 = (6 - 2)/2 = 2

the series is given by, 2, 4, 6, 8, 10

(ii)

when a = 4, d = (6 - a)/2 = (6 - 4)/2 = 1

the series is given by, 4, 5, 6, 7, 8

(iii)

when a = 8, d = (6 - a)/2 = (6 - 8)/2 = -2

the series is given by, 8, 6, 4, 2, 1