Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.

Question

8, 16, 32, ...
Write your answer using decimals and integers.
an = ____ (___)^n-1

Answer 1

The given sequence is 8, 16, 32, ...

To find the equation for this sequence, first observe that each term is a multiple of 8:

• 1st term: \( a_1 = 8 \)
• 2nd term: \( a_2 = 16 = 8 \times 2 \)
• 3rd term: \( a_3 = 32 = 8 \times 4 \)

The next step is identifying the pattern. Notice that each term can also be expressed as:

• \( a_1 = 8 \times 2^0 \)
• \( a_2 = 8 \times 2^1 \)
• \( a_3 = 8 \times 2^2 \)

From this, we can generalize the \( n \)-th term of the sequence as:

\[ a_n = 8 \times 2^{n-1} \]

Thus, the final equation is:

\[ a_n = 8 \times (2)^{n-1} \]