SELECT * FROM question_mgmt as q WHERE id=1065 AND status=1 SELECT id,question_no,question,chapter FROM question_mgmt as q WHERE courseId=2 AND subId=6 AND chapterId=80 and ex_no='5' AND status=1 ORDER BY CAST(question_no AS UNSIGNED)

Question:

The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

Answer:

Let a and r be the first term and the common ratio of the G.P. respectively.

∴ a = 1

a3 = ar2 = r2

a5 = ar4 = r4

∴ r2 + r4 = 90

⇒ r4 + r2 – 90 = 0

rightwards double arrow r squared space equals space fraction numerator minus 1 space plus space square root of 1 plus space 360 end root over denominator 2 end fraction equals fraction numerator minus 1 space plus-or-minus square root of 361 over denominator 2 end fraction equals fraction numerator minus 1 plus-or-minus 19 over denominator 2 end fraction equals minus 10 space o r space 9

∴ r = ± 3                                  ( Taking real roots)

Thus, the common ratio of the G.P. is ±3.


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