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.
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Answered by
1
Answer:
±3
Step-by-step explanation:
Let a and r be the first term and the common ratio of the G.P. respectively.
∴ a1 = 1
nth term of G.P is given by -
an = arn - 1
a3 = ar2 = (1)r2
a6 = ar4 = (1)r4
According to question -
a3 + a6 = 90
⇒ r2 + r4 = 90
⇒ r4 + r2 – 90 = 0
Assume r2 = t
⇒ t2 + t – 90 = 0
⇒ t2 + 10t - 9t – 90 = 0
⇒ t(t + 10) - 9(t + 10) = 0
⇒ (t - 9)(t + 10) = 0
∴ t =9 or t = - 10(invalid because t = r2, so t can't be - ve.)
∴ r2 = 9 ( Taking real roots)
∴ r = ±3
Thus, the common ratio of the G.P. is ±3.
JAI SHREE KRISHNA
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