Question

An arithmetic sequence has the terms a6=53 a 6 = 53 and a8=61 a 8 = 61 . Questions: What is the value of d d ? AnswerIncorrect What is the value

Answer 1

Answer:

The value of d is 4.

Step-by-step explanation:

It is given that the 6th term of an AP is $a_6=53$ and 8th term is $a_8=61$.

The nth term of an AP is

$a_n=a+(n-1)d$

6th term of an AP is $a_6=53$.

$a_6=a+(6-1)d$

$53=a+5d$              .... (1)

8th term is $a_8=61$.

$a_8=a+(8-1)d$

$61=a+7d$            .... (2)

Subtract equation (1) from equation (2).

$61-53=a+7d-(a+5d)$

$61-53=a+7d-a-5d$

$8=2d$

Divide both sides by 2.

$4=d$

Therefore the value of d is 4.

Answer 2

The given terms are two terms apart, so their difference is twice the difference of adjacent terms.

$a_8-a_6=2d=61-53=8\\\\d=\dfrac{8}{2}=4$

The value of d is 4.