NCERT Class 11 Mathematics Solutions: Chapter 9 –Sequences and Series Miscellaneous Exercise 9 Part 6
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Sum of a Geometric Series
1. A G.P. consists of an even number of terms. If the sum of all the terms is times the sum of terms occupying odd places, then find its common ratio.
Answer:
Consider the G.P. be .
Number of terms
According to the given condition,
Consider the G.P. be
So, the common ratio of the G.P. is .
2. The sum of the first four terms of an A.P. is . The sum of the last four terms is . If its first term is , then find the number of terms.
Answer:
The A.P. be a, .
Sum of first four terms
Sum of last four terms
According to the given condition,
[Since (given)]
So, the number of terms of the A.P. is