Question

Which term of the AP 72,63,,54.......0?

Answer 1

Answer :-

n = 9

Given:-

AP = 72, 63 , 54 ........ 0

To find :-

Which term of AP is 0.

Let nth term of AP will be 0.

Let a be the first term , D be the common difference and L be the last term.

We have,

a = 72

d = 63 - 72

d = -9

L = 0

Now, the formula of last term is given by :-

$\boxed{\sf{L = a + (n-1) d}}$

Now, put the given value,

→$0 = 72 + ( n -1)-9$

→$0 = 72 -9n +9$

→$0 = 81 -9n$

→$9n = 81$

→$n =\dfrac{81}{9}$

→$n = 9$

hence,

9 th term of given AP will be 0.

Answer 2

Formula for the term of an A.P.

An = A+(n-1)d

Where,

A= first term of AP

n= number of terms

d= common difference(A2-A1)

In the given question-

d= A2-A1

= 63-72

= -9

An =0

So

An= A+(n-1)d

0 = 72 + (n-1)(-9)

-72 = -9(n-1)

-72÷(-9) = (n-1)

8 = n-1

n = 9

Hence 0 will be the 9th term of the given AP