CBSE Class 10-Mathematics: Chapter – 5 Arithmetic Progressions Part 25 (For CBSE, ICSE, IAS, NET, NRA 2022)
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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 6th term
Using formula , to find nth 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 2nd and 6th term.
Using formula , to find nth 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 .