Question

Find the values of a,b and c,such that the no.s a,10,b,c,31 are in ap

Answer 1

Given,

A series of numbers a,10,b,c,31

To Find,

The value of a, b, and c such that it forms an A.P.

Solution,

Since, a,10,b,c,31 are in A.P

So,

a₅ = 31 = a+4d

a₂ = 10 = a+d

Subtacting the above equations

21 = 3d

d = 7

Putting the value of d in first equation

a+7 = 10

a = 3

So,

b = a+2d = 3+2(7) = 17

c = a+3d = 3+3(7) = 24

Hence, the value of a, b, and c is 3, 17, and 24 respectively.

Answer 2

Given,

A series of numbers a,10,b,c,31

To Find,

The value of a, b, and c such that it forms an A.P.

Solution,

Since a,10,b,c,31 are in arithmetic progression

$a_{n} = a + (n-1)d$

So,

a₅ = 31 = a + 4d

a₂ = 10 = a + d

Subtracting the above equations, we get

21 = 3d

d = 7

Putting the value of d in first equation

a + 7 = 10

a = 3

So,

b = a + 2d = 3 + 2(7) = 17

c = a + 3d = 3 + 3(7) = 24

Hence, the value of a, b, and c is 3, 17, and 24 respectively.