Question

how many terms are in the following AP 7 11 15.......483​

Answer 1

Given :-

$\sf\bullet { a\:=\:7}$

$\sf\bullet { d\:=\:4}$

$\sf\bullet { \ a_{n} \:=\:483}$

To find :-

$\sf\bullet {No. \: of\: Terms }$

Formula used !

$\bigstar{\boxed{\sf{ \ a_{n} \:=\:a+(n-1)d}}}$

Solution :-

$\sf{ \ a_{n} \:=\:a+(n-1)d}$

$\sf{ 483\:=\:7+(n-1)d}$

$\sf{ 476\:=\: (n-1)4}$

$\sf{ \frac{ \cancel{476}}{ \cancel{4}}\:=\:n-1}$

$\sf{119\:=\:n-1}$

$\sf{n\:=\:120}$

Answer 2

$\huge\boxed {Answer}$

There are n terms in following arithmetic

progression -

7 , 11 , 15 ,...............,483

Here ,

a = 7 , d = 4 , An = 483

An = a + (n - 1)d

483 = 7 + (n - 1)4

476 = 4(n - 1)

119 = n - 1

n = 120

So , There are 120 terms in above A.P.