NCERT Class 11-Math's: Chapter –9 Sequence and Series Part 11
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Question 14:
If are in A.P., whose common difference is , show that
Answer:
We have to prove that
Consider LHS
Now we have to find value of d in terms of so that further simplification can be made
As are in AP having common difference as
Hence
Take sin on both sides
Substitute appropriate value of for each term in LHS
We know that
Hence proved
Question 15:
If the sum of p terms of an A.P. is q and the sum of q terms is p, show that the sum of terms is . Also, find the sum of first terms .
Answer:
The sum of n terms of an AP is given by
Where a is the first term and d is the common difference
Given that
Subtract (i) from (ii) that is (ii) –(i)
Using
We have to show that
Using (m) and (n)
Substitute d from (iii)
Now we have to find sum of terms that is
Using (m) and (n)
Substitute d from (iii)
Hence sun of terms is