Question

Please show me step by step how to do this

Answer 1

Answer:

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

The 300th term of the sequence is 1197.

Step-by-step 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.

$r$ - Progression rate.

$n$ - 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:

$r = \frac{p(n)-p_{1}}{n-1}$

$r = 4$

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.