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Contents
Quiz
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Quiz
Arithmetic & Geometric
Progressions
1. If the first, third and
thirteenth terms of an arithmetic progression are in geometric progression, and
the sum of the fourth and seventh terms of this arithmetic progression is 40,
find the first term and the (non-zero) common difference.
2. The ninth, thirteenth and
fifteenth terms of an arithmetic progression are the first three terms of a
geometric progression whose sum of infinity is 80. The sixteenth term of an
arithmetic progression is equal to the fourth term of the geometric progression.
Calculate the sum of the first sixteen terms of the arithmetic progression.
3. An infinite geometric series
whose terms are positive has a finite sum. The ratio of the sum of the first
four terms to the sum of the first two terms is 13:9. Calculate the value of the
common ratio. If the fourth term is 1 7/9, calculate the sum to infinity. Find
the least value of n for which the sum to n terms differs from the sum to
infinity by less than 0.01.
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