The given terms are two terms apart, so their difference is twice the difference of adjacent terms.
[tex]a_8-a_6=2d=61-53=8\\\\d=\dfrac{8}{2}=4[/tex]
The value of d is 4.
Answer:
The value of d is 4.
Step-by-step explanation:
It is given that the 6th term of an AP is [tex]a_6=53[/tex] and 8th term is [tex]a_8=61[/tex].
The nth term of an AP is
[tex]a_n=a+(n-1)d[/tex]
6th term of an AP is [tex]a_6=53[/tex].
[tex]a_6=a+(6-1)d[/tex]
[tex]53=a+5d[/tex] .... (1)
8th term is [tex]a_8=61[/tex].
[tex]a_8=a+(8-1)d[/tex]
[tex]61=a+7d[/tex] .... (2)
Subtract equation (1) from equation (2).
[tex]61-53=a+7d-(a+5d)[/tex]
[tex]61-53=a+7d-a-5d[/tex]
[tex]8=2d[/tex]
Divide both sides by 2.
[tex]4=d[/tex]
Therefore the value of d is 4.
