Question

write the common difference of an AP ,whose nth term is 3n+5

Answer 1

we have nth term...

so,,first term,a1= 3*1+ 5= 8
a2 = 3*2 + 5= 11

Now, common difference, d= a2 - a1= 11 - 8= 3

Hope you get it

Answer 2

Given:

nth term is 3n+5

To Find:

the common difference of an AP.

Solution:

The nth term is given by $a_{n}$ = 3n + 5

We need two consecutive terms of the A.P., to find the common difference of the A.P.

Now, we will find the first and second terms of AP $a_{1} and a_{2}$ respectively.

Firstly, finding $a_{1}$

n = 1, putting the values in $a_{n}$ = 3n+5

$a_{1}$= (3×1+5)

  = 8

∴ $a_{1}$ = 8

$a_{2}$ = (3×2+5)

   = 11

∴ $a_{2}$ = 11

So, the common difference = d

The formula to find the common difference 'd' is d = $a_{2}- a_{1}$

 ⇒ d = $a_{2}$ - $a_{1}$

 ⇒ d = 11 - 8

 ⇒ d = 3

Therefore, the common difference is 3.