Question

If a,-3,b,5,c is in ap then the value of b is

Answer 1

Answer :

a = -7 , b = 1 , c = 9

Note : a = -7 , b = 1 , c = 9

★ A.P. (Arithmetic Progression) : A sequence in which the difference between the consecutive terms are equal is said to be in A.P.

★ If a1 , a2 , a3 , . . . , an are in AP , then

a2 - a1 = a3 - a2 = a4 - a3 = . . .

★ The common difference of an AP is given by ; d = a(n) - a(n-1) .

★ The nth term of an AP is given by ;

a(n) = a + (n - 1)d .

★ If a , b , c are in AP , then 2b = a + c .

Solution :

• Given AP : a , -3 , b , 5 , c
• To find : a = ? , b = ? , c = ?

Since a , -3 , b , 5 , c are in AP .

Thus ,

=> -3 , b , 5 are in AP

=> 2b = -3 + 5

=> 2b = 2

=> b = 2/2

=> b = 1

Also ,

=> a , -3 , b are in AP

=> 2•(-3) = a + b

=> -6 = a + 1

=> a = -6 - 1

=> a = -7

Also ,

=> b , 5 , c are in AP

=> 2•5 = b + c

=> 10 = 1 + c

=> c = 10 - 1

=> c = 9

Hence ,

a = -7 , b = 1 , c = 9