Question

Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.


10 , 20 , 40 , ...


Write your answer using decimals and integers.

an =
(
)n - 1

Answer 1

The given sequence is: 10, 20, 40, ...

To find an equation for this sequence, we first observe the pattern.

1. The first term (n = 1): \( a_1 = 10 \)
2. The second term (n = 2): \( a_2 = 20 \)
3. The third term (n = 3): \( a_3 = 40 \)

We can see that each term in the sequence is double the previous term. More explicitly:

- \( a_2 = 2 \times a_1 = 2 \times 10 = 20 \)
- \( a_3 = 2 \times a_2 = 2 \times 20 = 40 \)

Therefore, it appears that the sequence can be described by the recurrence relation:

- \( a_n = 2 \times a_{n-1} \)

If we want to express \( a_n \) directly in terms of \( n \), we can see that:

- The \( n \)-th term can be written in terms of powers of 2:

\[
a_n = 10 \times 2^{n-1}
\]

Thus, the equation to describe the sequence is:

\[
a_n = 10 \times 2^{n - 1}
\]