Question

There are five terms in an arithmetic Progression. The sum of these terms is 55 and

the 4th term is 5 more than the sum of the first two terms. Find the terms of the A.P.​

Answer 1

Answer:

3, 7, 11, 15, 19, .. is the A.P.

Step-by-step explanation:

5 terms in an Arithmetic Progression are consecutive.

a, (a + d), (a + 2d), (a + 3d), (a + 4d) are the 5 terms.

Sum of these terms = 55

a + a + d + a + 2d + a + 3d + a + 4d = 55

5a + 10d = 55

Dividing the equation throughout by 5, we get,

1. a + 2d = 11

4th term is 5 more than the sum of the first two terms

a + 3d = 5 + {(a) + (a + d)}

a + 3d = 5 + (2a + d)

a + 3d = 5 + 2a + d

2a - a + d - 3d = -5

2. a - 2d = -5

Adding equation 1 and 2, we get,

  a + 2d = 11

+ a - 2d = -5

2a = 6

a = 6/2

a = 3

Substituting a = 3 in equation 1, we get,

a + 2d = 11

3 + 2d = 11

2d = 11 - 3

2d = 8

d = 8/2

d = 4

First term = a = 3

Second term = a + d = 3 + 4 = 7

Third term = a + 2d = 3 + 2(4) = 11

Fourth term = a + 3d = 3 + 3(4) = 15

Fifth term = a + 4d = 3 + 4(4) = 19

3, 7, 11, 15, 19, .. is the A.P.