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Calculate the sum of the series 4 + 12 + 36 + ... + 2916.
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The sequense 4, 12, 36, . . ., 2916 is a geometric progression
with the first term a= 4 and the common ratio of r= 3
(sinse 12/4 = 3 and the ratio of each next term to the current term is 3).
Find the number of term. Use the formula for the n-th term
2916 = .
It gives 2916/4 = 729 = . But 729 = ; therefore, n-1 = 7 and n= 7.
CHECK. = use your calculator = 2916, correct.
To find the sum of this GP, use the general formula for the sum of a GP
= .
It gives at n= 7
= = = = use your calculator = 4372. ANSWER
Solved.
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On geometric progressions, see introductory lessons
- Geometric progressions
- The proofs of the formulas for geometric progressions
- Problems on geometric progressions
- Word problems on geometric progressions
in this site.
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