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Question
Find the sum to indicated number of terms in the geometric progressions x3, x5, x7, ... n terms (if x ≠ ± 1).
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Solution
geometric progressions x3, x5, x7, …..
First term, a = x3, common ratio, r = `"x"^5/"x"^3 = "x"^2`
∴ Sum of n terms = `("a"(1 - "r"^"n"))/(1 - "r")`
= `("x"^3 xx [1 - ("x"^2)^"n"])/(1 - "x"^2)`
= `("x"^3 xx [1 - "x"^(2"n")])/(1 - "x"^2)`
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