Question

Find the 1000th term of the sequence 3, 4, 5, 6 ……….

Answer 1

Hint: In this question, we use the concept of Arithmetic progression. We have to use the formula of nth term of an A.P ${a_n} = a + \left( {n - 1} \right)d$ where $a$ is a first term, $d$ is a common difference of an A.P and $n$ is a number of terms in an A.P.

Complete step-by-step answer:
Given, the sequence 3, 4, 5, 6 ……….
First we check if the given sequence is Arithmetic progression or not.
Now, the common difference of given sequence is $d = 4 - 3 = 5 - 4 = 6 - 5 = 1$
So, it’s proved that the given sequence is A.P with common difference 1.
First term of an A.P $a = 3$ and the common difference of an A.P $d = 1$
Now, to find the 1000th term of the sequence so we have to use the formula of the nth term of an A.P.
So, nth term of an A.P is ${a_n} = a + \left( {n - 1} \right)d$
For the 1000th term, the value of a=3, d=1 and n=1000.
$
   \Rightarrow {a_{1000}} = 3 + \left( {1000 - 1} \right) \times 1 \\
   \Rightarrow {a_{1000}} = 3 + 999 \\
   \Rightarrow {a_{1000}} = 1002 \\
$
Hence, the 1000th term of the sequence is 1002.

Note: Whenever we face such types of problems we use some important points. First we check if the given sequence is Arithmetic progression or not by using the common difference then find the value of first term, common difference and number of terms in an A.P. So, after using the formula of the nth term of an A.P we will get the required answer.