Question

Which term of the ap 51,47,43 ......is a cube of itself?

Answer 1

Heyy mate ❤✌✌❤

Here's your Answer.....

Answer 2

The $14^{th}$ term which is -1 will be the cube of itself.

Given:

The arithmetic progression, 51,47,43 ......

To find:

The term of the given arithmetic progression is the cube of itself.

Solution:

We know that only 1 and -1 are the two numbers that have a cube the number itself.

We know that the $n^{th}$ term of the arithmetic progression is given by,

$t_{n} =a+ (n-1)*d$                                 ...(I)

In the given arithmetic progression,

There are two possibilities for $t_{n}= -1$ or $t_{n}= 1$.

Consider $t_{n}= -1$,

• $t_{n}= -1$  
• a=51
• d= next term - immediate previous term = 47 - 51 = - 4

From (I),

   -1 = 51 + ( n-1)*(-4)

⇒ -1 = 51 -4n + 4                                           ...(II)

rearranging above,

   4n-56=0

⇒ 4(n-14)=0

⇒ n-14=0

⇒ n=14

So the above formula worked for  $t_{n}= -1$.

It will not work for  $t_{n}= 1$ as we won't have -1 to get the value of n, as the further solution follows from equation (II)

Hence, The $14^{th}$ term which is -1 will be the cube of itself.

#SPJ2