CBSE Class 10-Mathematics: Chapter – 5 Arithmetic Progressions Part 17 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 16:

Find the sum of first terms of the list of no. whose term is given by

Answer:

Put

4 Mark Questions

Question 1:

For the following Aps, write the first term and the common difference.

(i)

(ii)

(iii)

(iv)

Answer:

(i)

First term Common difference (d) Second term – first term

Third term – second term and so on

Therefore, Common difference (d)

(ii)

First term Common difference (d) Second term Firstterm

Third term – Second term and so on

Therefore, Common difference (d)

(iii)

First term

Common difference Second term – First term = Third term – Second term and so on

Therefore, Common difference

(iv)

First term Common difference (d) = Second term – First term

= Third term – Second term and so on

Therefore, Common difference (d)

Question 2:

The 17th term of an AP exceeds its 10thterm by . Find the common difference

Answer:

(i) We need to show that form an AP where

Let us calculate values of using

So, the sequence is of the form

Let us check difference between consecutive terms of this sequence.

Therefore, the difference between consecutive terms is constant which means terms

We have sequence

First term and Common difference

Applying formula, to find sum of n terms of AP, we get

Therefore, sum of first terms of AP is equal to .

(ii)

We need to show that form an AP where

Let us calculate values of using

So, the sequence is of the form

Let us check difference between consecutive terms of this sequence.

Therefore, the difference between consecutive terms is constant which means terms form an AP.

We have sequence

First term and Common difference

Applying formula, to find sum of n terms of AP, we get

Therefore, sum of first terms of AP is equal to .