CBSE Class 10-Mathematics: Chapter – 5 Arithmetic Progressions Part 25 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Question 24:

In the following AP՚s find the missing terms:

(i)

(ii)

(iii)

(iv)

(v)

Answer:

(i)

We know that difference between consecutive terms is equal in any A. P.

Let the missing term be .

Therefore, missing term is .

(ii)

Let missing terms be and .

The sequence becomes

We know that difference between consecutive terms is constant in any A. P.

And

But we have ,

Therefore, missing terms are 18 and 8.

(iii)

Here, first term And, term

Using formula , to find term of arithmetic progression,

Therefore, we get common difference

Second term

Third term second term

Therefore, missing terms are

(iv)

Here, First term and 6^th term

Using formula , to find n^th term of arithmetic progression,

Therefore, common difference

Second term first term

Third term second term

Fourth term third term

Fifth term fourth term

Therefore, missing terms are and .

(v)

We are given 2^nd and 6^th term.

Using formula , to find n^th term of arithmetic progression,

These are equations in two variables, we can solve them using any method.

Using equation , we can say that .

Putting value of a in equation ,

Using this value of d and putting this in equation ,

Therefore, we get and

First term

Third term second term

Fourth term third term

Fifth term fourth term

Therefore, missing terms are and .