Question

If in an A.P., d=10, what will be the value of ${{t}_{6}}-{{t}_{2}}$ i.e. the difference of the 6th and the 2nd term?

Answer 1

Hint: In this question, we are considering an arithmetic progression or A.P. Therefore, we should know about the general expression of the terms of an A.P. and then take the 6th and the 2nd term whose difference will give us the required answer.

Complete step-by-step answer:
In an arithmetic progression, the next term of the sequence of numbers is obtained by adding a common difference d to the previous term. Thus the sequence will be as:
$\text{a, a+d, a+2d, a+3d,}....$
Thus, if the nth number of the arithmetic progression is given by ${{a}_{n}}$, then it can be represented by the general formula as
${{t}_{n}}=a+(n-1)d$
Thus, the 2nd and the 6th term can be expressed in the form
${{t}_{2}}=a+(2-1)d=a+d$
and
${{t}_{6}}=a+(6-1)d=a+5d$
Thus, we can obtain the difference of the 6th and the 2nd term as
${{t}_{6}}-{{t}_{2}}=\left( a+5d \right)-(a+d)=a-a+5d-d=4d$
Therefore, the required answer will be 4d. As d is given here to be 10, we get the difference of the 6th and the 2nd term of the A.P. as
${{t}_{6}}-{{t}_{2}}=4d=4\times 10=40$
Thus, the required answer of the question should be 40.

Note: We should note that in this case as the difference of two terms is taken, the first term i.e. a gets cancelled out, thus we do not need the first term of the A.P. to solve the question.