NCERT Class 11 Mathematics Solutions: Chapter 9 – Sequences and Series Miscellaneous Exercise 9 Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)
Glide to success with Doorsteptutor material for IMO : fully solved questions with step-by-step explanation- practice your way to success.
1. The terms of an A. P. are respectively. Show that
Answer:
Consider be the first term and the common difference of the A. P. respectively.
The nth term of an A. P. is given by,
So,
… eq (1)
… eq (2)
… eq (3)
Subtracting equation (2) from (1) , we obtain
… eq (4)
Subtracting equation (3) from (2) , we obtain
… eq (5)
Equating both the values of d obtained in (4) and (5) ,
(By rearranging terms)
So, the given result is proved.
2. If are in A. P. , prove that are A. P.
Answer:
It is given that are in A. P.
So, are in A. P.