Answer:
Second term of this sequence: [tex]10[/tex].
Third term of this sequence: [tex]20[/tex].
Step-by-step explanation:
The first step is to find the common ratio of this sequence.
In a geometric sequence, multiply one term by the common ratio to find an expression for the next term. Let [tex]r[/tex] denote the common ratio of this sequence. For this sequence:
- The first term of this sequence is [tex]5[/tex].
- Multiply the first term by the common ratio to find an expression for the third term: [tex]5\, r[/tex].
- Multiply the second term by the common ratio to find an expression for the fourth term: [tex]5\, r^{2}[/tex].
- Similarly, an expression for the the fourth term would be: [tex]5\, r^{3}[/tex].
However, the question states that the value of the fourth term is [tex]40[/tex]. In other words, [tex]5\, r^{3} = 40[/tex].
Solve this equation for [tex]r[/tex]:
[tex]r^{3} = 8[/tex].
[tex]r = 2[/tex].
(Since the power of [tex]r[/tex] is non-even in the equation, there's no need to consider the sign of [tex]r\![/tex] when taking the cube root.)
Substitute [tex]r = 2[/tex] into the expression for the second term and the third term to find their values:
- Second term: [tex]5\, r = 10[/tex].
- Third term: [tex]5\, r^{2} = 20[/tex].
