Question

3. In the following APs, find the missing terms in the boxes
_,13,_,3
​

Answer 1

Answer :

a = 18 , b = 8

Note :

★ 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 :

Let the missing terms be x and y , so that AP becomes : a , 13 , b , 3 .

Since the given sequence is AP , thus 13 , b , 3 are in AP .

Hence ,

=> 2b = 13 + 3

=> 2b = 16

=> b = 16/2

=> b = 8

Also ,

a , 13 , b are in AP , hence

=> 2•13 = a + b

=> 26 = a + 8

=> a = 26 - 8

=> a = 18

Hence ,

a = 18 , b = 8

Answer 2

Answer:

• let, a1=x. and a3=y then,,. 13-x=y-13. (1). and, y-13=3-y. (2). Now,. from(2). y= 8. and value of y, put in (1) then, x=18. then, sequence is 18 , 13 , 8 , 3.