Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.

Question

13 , 26 , 52 , ...

Write your answer using decimals and integers.

an =
(
)n - 1

Answer 1

The sequence you've provided is $13,26,52,\dots$. Observing the sequence, each term is double the previous term.

To express the sequence as an equation in terms of $n$ (where $n$ represents the position of the term, with $n=1$ for the first term), we can identify that:

• The first term ($n=1$) is $13$.
• The second term ($n=2$) is $26$, which is $13\times 2$.
• The third term ($n=3$) is $52$, which is $13\times 2^2$.

From this pattern, we can see that each term can be described by the formula:

$$a_n=13\times 2^{n-1}$$

This means for any $n$:

• When $n=1$, $a_1=13\times 2^0=13$.
• When $n=2$, $a_2=13\times 2^1=26$.
• When $n=3$, $a_3=13\times 2^2=52$.

Thus the equation for the sequence is:

$$a_n=13\times 2^{n-1}$$