Please show me step by step how to do this

Question

asked Jan 18, 2022 40.0k views

1 Answer

Scatman · Answer 1 · 2022-01-24T17:04:19+0000

Answer:

The next three terms of the sequence are 17, 21 and 25.

The 300th term of the sequence is 1197.

Explanation:

The statement describes an arithmetic progression, which is defined by following formula:

$p(n) = p_(1)+r\cdot (n-1)$ (1)

Where:

p_(1) - First element of the sequence.

- Progression rate.

- Index of the n-th element of the sequence.

p(n) - n-th element of the series.

If we know that
p_(1) = 1 ,
n = 2 and
p(n) = 5 , then the progression rate is:

r = (p(n)-p_(1))/(n-1)

r = 4

The set of elements of the series are described by
$p(n) = 1 + 4\cdot (n-1)$ .

Lastly, if we know that
n = 300 , then the 300th term of the sequence is:

$p(n) = 1 + 4\cdot (n-1)$

p(n) = 1197

And the next three terms of the sequence are:

n = 5

$p(n) = 1 + 4\cdot (n-1)$

p(n) = 17

n = 6

$p(n) = 1 + 4\cdot (n-1)$

p(n) = 21

n = 7

$p(n) = 1 + 4\cdot (n-1)$

p(n) = 25

The next three terms of the sequence are 17, 21 and 25.

The 300th term of the sequence is 1197.