Question

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

Answer 1

Hint: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 \[d\].