# Find the first five terms in sequences with the following nth terms. a. n^2 + 2 b. 6n +1 c....

## Question:

Find the first five terms in sequences with the following nth terms.

{eq}\begin{align*} a&. n^2 + 2 \\[0.3 cm] b&. 6n +1 \\[0.3 cm] c&. 10^n-9 \\[0.3 cm] d&. 5n-2 \end{align*} {/eq}

## Sequences

Sequences in mathematics are are are a group of terms where the {eq}n^{th} {/eq} term of the group can be described using an equation. The two major sequences are arithmetic progressions where the major difference between consecutive terms is constant and is known as the common difference. The second major sequence is the geometric progression where the ratio of consecutive terms is always the same and known as the common ratio.

## Answer and Explanation: 1

Here we know the equation of the {eq}n^{th} {/eq} term.

We can simply substitute 1,2,3,4 and 5 to find the first 5 terms.

{eq}\begin{align*} a&. n^2 + 2 \\[0.3 cm] a(1) = 3\\ a(2) = 6\\ a(3) = 11\\ a(4) = 18\\ a(5) = 27\\ b&. 6n +1 \\[0.3 cm] a(1) = 7\\ a(2) = 13\\ a(3) = 19\\ a(4) = 25\\ a(5) = 31\\ c&. 10^n-9 \\[0.3 cm] a(1) = 1\\ a(2) = 91\\ a(3) = 991\\ a(4) = 9991\\ a(5) = 99991\\ d&. 5n-2 a(1) = 3\\ a(2) = 8\\ a(3) = 13\\ a(4) = 18\\ a(5) = 23\\ \end{align*} {/eq}

#### Learn more about this topic:

from

Chapter 21 / Lesson 1In this lesson, explore an introduction to sequences in mathematics and discover the two types of math sequences: finite and infinite. Review examples.