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

Second term of this sequence: .

Third term of this sequence: .

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

However, the question states that the value of the fourth term is . In other words, .

Solve this equation for :

.

.

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

Substitute into the expression for the second term and the third term to find their values:

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y