Give the exponential seq of 1/8, m, n, 1/512. Find m, n.

Question

ScanSolve AI Tutor · Accepted Answer

The given sequence is a Geometric Progression (GP): $\frac{1}{8}, m, n, \frac{1}{512}$ .
Let the first term be $a$ and the common ratio be $r$ .
The terms of a GP are $a, ar, ar^2, ar^3, \dots$

Identify the first term and the fourth term.
The first term is $a = \frac{1}{8}$ .
The fourth term is $ar^3 = \frac{1}{512}$ .
Find the common ratio ( $r$ ).
Substitute the value of $a$ into the equation for the fourth term:
$\frac{1}{8} r^3 = \frac{1}{512}$
Multiply both sides by 8:
$r^3 = \frac{8}{512}$
Simplify the fraction:
$r^3 = \frac{1}{64}$
Take the cube root of both sides:
$r = \sqrt[3]{\frac{1}{64}}$ $r = \frac{1}{4}$
Find the value of $m$ .
The second term is $m = ar$ .
$m = \frac{1}{8} \times \frac{1}{4}$ $m = \frac{1}{32}$
Find the value of $n$ .
The third term is $n = ar^2$ .
$n = \frac{1}{8} \times \left(\frac{1}{4}\right)^2$ $n = \frac{1}{8} \times \frac{1}{16}$ $n = \frac{1}{128}$
The values are $m = \frac{1}{32}, n = \frac{1}{128}$ .

Give the exponential seq of 1/8, m, n, 1/512. Find m, n.

Answer

Step-by-step solution

Identify the first term and the fourth term.

Find the common ratio ( $r$ ).

Find the value of $m$ .

Find the value of $n$ .

Try one yourself

Still stuck on this one?

Give the exponential seq of 1/8, m, n, 1/512. Find m, n.

Answer

Step-by-step solution

Identify the first term and the fourth term.

Find the common ratio (rrr).

Find the value of mmm.

Find the value of nnn.

Try one yourself

Still stuck on this one?

Find the common ratio ( $r$ ).

Find the value of $m$ .

Find the value of $n$ .