Question

If nth term of an AP is 5-3n then find the common difference?

Answer 1

Answer:

$\huge\star \underline{ \boxed{ \purple{Answer}}}\star$

Common difference required here = 3

Step-by-step explanation:

GIVEN :-

nth term of an AP is 5-3n

TO FIND :-

the common difference?

SOLUTION :-

let the common difference be d.

it is given that,

➝$\sf{a_n\:=\:5\:-\:3n}$

Now,

➝$\sf{a_{n-1}\:=\:5\:-\:3(n-1)}$

➝$\sf{5\:-\:3n\:+\:3}$

➝$\sf{8\:-\:3n}.,.,.,.,.,.,.,.,.,.,.,.,.eq^n(i)$

NOW,

Lets calculate common difference

➝$\sf{d\:=\:a{n-1}\:-\:a{n}}$

➝$\sf{d\:=\:(8\:-\:3n)\:-\:(5\:-\:3n)}$

➝$\sf{d\:=\:8\:\cancel{-3n}\:-5\:\cancel{+3n}}$

➝$\sf{d\:=\:8\:-\:5}$

➝$\sf{d\:=\:3}$

Hence,

the required common difference here is , 3.

$\Large\mathcal\red{Hope \: it \: helps \: you\:friend}$

Answer 2

Answer:

Common difference = t2 - t1

Step-by-step explanation:

It is given that ,

nth term of an A.P = 5 - 3n

tn = 5 - 3n

t1 = 5 - 3 × 1 = 2

t2 = 5 - 3 × 2 = -1

t3 = 5 - 3 × 3 = - 4

Therefore ,

Common difference = t2 - t1

d = - 1 - 2

d = -3

Hope it helps you:)