Question 1184936
Given two specific terms of geometric sequence. Find the common ratio and first term. Show the solution. 


a(2)=4 ; a(5)=32

please can you teach me the step by step because I really can't understand T-T
<pre>The easiest method is to calculate r, or common ratio: {{{root (matrix(1,3, Higher, Term, number) - matrix(1,3, Lower, Term, number),  matrix(1,3, Higher, Term, value)/matrix(1,3, Lower, Term, value))}}} 
This becomes: {{{root (5 - 2, 32/4)}}}, and then: {{{matrix(1,3, root (3, 8), "=", 2)}}}

With common ratio being 2, and using the 2nd term, 4, we get: {{{highlight_green(matrix(4,3, a[n], "=", a[1]r^(n - 1), a[2], "=", a[1](2)^(2 - 1), 4, "=", a[1](2), 4/2, "=", a[1]))}}}

                                                First term or {{{highlight_green(matrix(1,3, a[1], "=", 2))}}}

OR

<b><u>The LONGER method:</b></u>
Use the equation for a term of a GP, which is: {{{matrix(1,3, a[n], "=", a[1]r^(n - 1))}}}, and the 2nd term (4) to find an equation in {{{matrix(1,3, a[1], and, r)}}}
Repeat the process but this time, use 5th term (32) to find an equation in {{{matrix(1,3, a[1], and, r)}}}
You will then have a system of equations in {{{matrix(1,3, a[1], and, r)}}}, which you then solve to get the values of the 1st term (a<sub>1</sub>), and r, the common ratio.</pre>