Question

if X + 2, x^2 - 2, 3x is an ap then the 5th term will be ​

Answer 1

Answer:

Step-by-step explanation:

X^2 + 5 .................

Answer 2

Concept

The Arithmetic Progression (AP) is a numerical sequence in which the difference between any two successive numbers is always the same.

Given

The terms $x+2,x^2-2,3x$are arranged in mathematical order.

Find

We have to find the $5th$in terms of progression

Solution

First, we'll determine the value of $x$ by multiplying two terms and equal the third term

$x^2-2=\frac{x+2+3x}{2}$

$\Rightarrow x^2-2=2x+1$

$\Rightarrow x^2-2x-3=0$

$\Rightarrow x=3,-1$

When $x=3$.

The first three terms are$5,7,9$ then $a=5$ and the common difference is $d=2$.

Now, the fifth term is

$a+4d=5+4(2)=13$

When $x=-1$then the first three terms are $1,-1,-3$and the common difference is $d=-2$

Now, the fifth term is

$a+4d=1+4(-2)=-7$

Hence, the $5th$ term of ap is $13$ when $x=3$ and $-7$ when $x=-1$

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