Question

If the 7th term of an ap is 49 and the 17th term of an ap is 289, find the n terms of an ap

Answer 1

7th term = 49


a + ( 7 - 1 )d = 49


a + 6d = 49


a = 49 - 6d -----: ( 1 )




17th term = 289


a + ( 17 - 1 )d = 289


a + 16d = 289


a = 289 - 16d ------: ( 2 )




Comparing both the equations :


49 - 6d = 289 - 16d


16d - 6d = 289 - 49


10d = 240


d = 24



Substituting the value of d in ( 1 ) :


a = 49 - 6d


a = 49 - 6( 24 )


a = 49 - 144


a = - 95



Therefore,


nth term = a + ( n - 1 )d


nth term = - 95 + ( n - 1 )( 24 )


nth term = - 95 + 24n - 24


nth term = 24n - 119
$\:$

Answer 2

What's a ?

=> a is the first term of the AP .

What's d ?

=> d is the common difference between the terms.

AP stands for Arithmetic Progressions.

How to write an Arithmetic Progression with the help of first term 'a' and common difference 'd'?

=> Arithmetic Progression -

a , a+d , a+2d , a+3d , a+4d ...

What is an Arithmetic Progression?

A sequence whose terms increase or decrease by fix number is called arithmetic progression.

And this fix number is - 'd' aka common difference between the terms.