Question

In a GP, first term is 1. If 4T, + 5T, is minimum, then its common ratio is
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Answer 1

Given: In a GP, first term is 1. If 4T2, + 5T3, is minimum

To find: Its common ratio i?

Solution:

• Now we have given that the first term is 1.

• The series in GP is:

                  a, ar, ar², ar³ ..............

• Putting a = 1, we get:

                  1, r, r², r³ ................

• In this, we have T2 = r and T3 = r².

• So putting these values in given term:

                  4T2, + 5T3 = 4(r) + 5(r²)

• Consider it as x, so:

                  x = 4r + 5r²

• Differentiating it w.r.t. r, we get:

                  dx/dr = 4 + 2(5r)

• Now we have given that x is munimun, so:

                  dx/dr = 4 + 10r = 0

                  10r = -4

                  r = -2/5

Answer:

               So the common ratio is -2/5.

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