NCERT Class 11 Mathematics Solutions: Chapter 9 –Sequences and Series Miscellaneous Exercise 9 Part 6

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Sum of a Geometric Series

Sum of a Geometric Series

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