Question

How do you write the first five terms of a sequence $a_{n} = 5n – 3$ ?

Answer 1

In this question, we need to find the first five terms of a sequence $a_{n} = 5n – 3$ . A Sequence is defined as a collection of elements in which repetitions are also allowed whereas a series is the sum of all the elements in the sequence. In order to find first five terms of the sequence $a_{n} = 5n – 3$ put the value of $n$ from $1$ to $5$ one by one to find the values of $a_{1},\ a_{2},\ a_{3},\ a_{4}$ and $a_{5}$ . By observing the given term , it is an arithmetic sequence . First , we need to substitute $n = 1,\ 2,\ 3,\ 4,\ 5\$ one by one to the first five terms.

Complete step by step answer:
Given, $a_{n} = 5n - 3$. We need to find the first five terms of the sequence $a_{1},\ a_{2},\ a_{3},\ a_{4}$ and $a_{5}$. We can substitute $n = 1,\ 2,\ 3,\ 4,\ 5$ one by one to first five
terms.Now we can substitute $n = 1$ ,
$a_{1} = 5\left( 1 \right) - 3$
On simplifying we get,
$a_{1} = 2$
Then we can substitute $n = 2$ ,
$a_{2} = 5\left( 2 \right) - 3$
On simplifying we get,
$a_{2} = 7$
Then we can substitute $n = 3$ ,
$a_{3} = 5\left( 3 \right) - 3$

On simplifying we get,
$a_{3} = 12$
Now we can substitute $n = 4$,
$a_{4} = 5\left( 4 \right) - 3$
On simplifying, we get,
$a_{4} = 17$
Finally, we can substitute $n = 5$ ,
$a_{5} = 5\left( 5 \right) - 3$
On simplifying, we get,
$a_{5} = 22$

Therefore the first five terms of the sequence $a_{n} = 5n - 3$ are $2,\ 7,\ 12,\ 17\ ,22$.

Note: We have found the first five terms of the sequence $a_{n} = 5n – 3$ are $2,\ 7,\ 12,\ 17\ ,22$ . By observing the terms of the sequence , we can clearly say that the given sequence is an arithmetic sequence with the first term $a = 2$ with common difference $d = 5$ . A sequence is said to be an arithmetic sequence, if the difference of a term and the previous term are always the same. The first term of the arithmetic sequence is denoted by the letter $a$ and the common difference is denoted by the letter $d$.