Sum of all odd terms of a GP containing 100 terms is 1122 and the sum of all even terms of the same GP is 1683. Find the common ratio.
Explanation:
Sum of odd terms of a GP with first term a and common ratio = r is a + ar2 + ar4 + ar6 + … + ar98 = 1122 …(1)
Sum of even terms of a GP with first term a and common ratio = r is ar + ar3 + ar5 + ar7 + … + ar99 = 1683 …(2)
Dividing (2) by (1), ar+ar3+ar5+ar7+…+ar99a+ar2+ar4+ar6+…+ar98 = 16831122
∴ ar1+r2+r4+ar6+…+ar98a1+r2+r4+r6+…+ar98 = 32
∴ r = 32
Hence, option (c).
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