Question

The first term with a geometric sequence with positive terms is 80. If the first three terms are 185, then what is the common ratio?

Answer 1

Answer:

0.75

Step-by-step explanation:

Let us assume that the first term of the G.P. is a and the common ratio is r.

So the terms of the G.P. are: a, ar, ar², ar³..... so on.

Given that the first term of the G.P.,  a=80, and the sum of the first three terms =185 and the G.P. is with all positive terms. ........ (1)

We have to find out the common ratio r of the G.P.

So, according to the condition (1)

a + ar + ar² =185

⇒a(1+r+r²)=185

⇒80(1+r+r²)=185

⇒r²+r+1 =2.3125

⇒r²+r-1.3125 =0

⇒$r=\frac{-1+\sqrt{1+4*1.3125}}{2}$ { Ignoring the negative root as all the terms in the G.P. are positive)

⇒$r=\frac{-1+2.5}{2}$

⇒r=0.75 (Answer)