Question

if 3x, X + 2 and 8 are three consecutive terms of an A.P.,find its fourth term

Answer 1

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Answer 2

Solution :

An arithmetic Progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term expect the first term

Let 3x , x + 2 and 8 are in A.P.

Where ,  3x = a1

⇒ x + 2 = a2

⇒ 8 = a3

Finding the value of x

$a_2 - a_1 = a_3 - a_2$

⇒ $x + 2 - 3x =  8 - ( x + 2)$

⇒ $2 - 2x = 6 - x$

⇒ $x = -4$

Finding first term , Second term and the Common difference

a1 = 3x

Putting the value of x

⇒ 3 * (-4)

⇒ - 12

a2 = x + 2

⇒ -4 + 2

⇒ -2

Common Difference

a2 - a1

⇒ -2 - (-12)

⇒ 10

Since , we have a and d we can easily find the fourth term

$a_4 = a + ( n - 1) d$

⇒ $-12 + ( 4 - 1) * 10$

⇒ $-12 + 3 * 10$

⇒ $-12 + 30$

⇒ 18

Therefore , the fourth term of an A.P. is 18