Question

Match the type of sequence to the appropriate example

Answer 1

Step-by-step explanation:

1)

Considering the sequence

2, 9, 16, 23,...

This sequence is an arithmetic sequence as the common difference between consecutive terms is constant.

i.e. $d = 9-2 = 7$, $d = 16-9 = 7$, $d = 23-16 = 7$

2)

Considering the sequence

3, 15, 75, 375,...

This sequence is geometric sequence as the common ratio between consecutive terms is constant.

i.e. r = 15/3 = 5, r = 75/15 = 5

3)

Considering the sequence

0,4,4,8,...

This sequence is not in arithmetic sequence as the common difference is not same.

This sequence is also not in geometric sequence as the common ratio is not same.

As the 2nd and 3rd term is repeating, it means the next term i.e. 5th would be 8 as the 4th term is 8.

So, it will be a recursive sequence.

4)

$y=(1.1)^{x}$

As the base of this exponential function is greater than 1.

i.e. $base>1$ because 1.1 > 1.

Therefore, this function will have exponential growth.

5)

$y=(\frac{1}{4})^{x}$

As the base of this exponential function is less than 1. i.e. $base$ because 1/4 < 1.

Therefore, this function will have exponential decay.

Keywords: exponential decay, exponential growth, arithmetic sequence, geometric sequence, recursive sequence

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