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CBSE Class 10- Mathematics: Chapter β 5 Arithmetic Progressions Part 17
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 β first term
Third term β second term and so on
Therefore, Common difference (d)
(ii)
First term
Common difference (d) Second term Firstterm
Third term β Second term and so on
Therefore, Common difference (d)
(iii)
First term
Common difference Second term β First term = Third term β Second term and so on
Therefore, Common difference
(iv)
First term
Common difference (d) = Second term β First term
= Third term β 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 .