You visited us 4 times! Enjoying our articles? Unlock Full Access!

Common Ratio

The first ter...

Question

The first term of the geometric progression $b_{1}, b_{2}, b_{3}, . . .$ is unity. For what value of the common ratio of the progression is $4 b_{2} + 5 b_{3}$ at a minimum?

Open in App

Solution

given $b_{1} = 1$
$⟹ 4 b_{2} + 5 b_{3} = 4 r + 5 r^{2}$ where r is common ratio
A quadratic equation has a minimum value at x=-b/2a $⟹ 4 b_{2} + 5 b_{3}$ has minimum value at $r = - 0.4$

Suggest Corrections

Similar questions

b_{1}, b_{2}, b_{3}, \dots

4 b_{2} + 5 b_{3}

1, b_{2}, b_{3}, . . .

4 b_{2} + 5 b_{3}

b_{1}, b_{2}, b_{3}, \dots

b_{1} = 1,

4 b_{2} + 5 b_{3}

a, a_{1}, a_{2}, a_{3}, . . . . . . . . .

b, b_{1}, b_{2}, b_{3}, . . . . . . . . .

l o g a_{n} - b_{n} = l o g a - b

β

a

r

S

a

2 r

3 S

r

Join BYJU'S Learning Program