Question

Determine the 2nd and 3rd terms of a geometric sequence of which T1 =5 and T4=40​

Answer 1

Second term of this sequence:
`10`.

Third term of this sequence:
`20`.

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
`r` denote the common ratio of this sequence. For this sequence:

• The first term of this sequence is
  `5`.
• Multiply the first term by the common ratio to find an expression for the third term:
  `5\, r`.
• Multiply the second term by the common ratio to find an expression for the fourth term:
  `5\, r^(2)`.
• Similarly, an expression for the the fourth term would be:
  `5\, r^(3)`.

However, the question states that the value of the fourth term is
`40`. In other words,
`5\, r^(3) = 40`.

Solve this equation for
`r`:

`r^(3) = 8`.

`r = 2`.

(Since the power of
`r` is non-even in the equation, there's no need to consider the sign of
`r\!` when taking the cube root.)

Substitute
`r = 2` into the expression for the second term and the third term to find their values:

• Second term:
  `5\, r = 10`.
• Third term:
  `5\, r^(2) = 20`.