Question

If (x + 1), 3x and (4x + 2) are first three terms of an A.P. then its 5"term is -​

Answer 1

$\huge \boxed{ \fcolorbox{cyan}{red}{Answer : }}$

Given

If (x + 1), 3x and (4x + 2) are first three terms of an A.P. then its 5th term is

Answer

$\sf{3x - (x + 1) = (4x + 2) - 3x}$

$\sf{3x - x - 1 = 4x + 2 - 3x}$

$\sf{2x - 1 = x + 2}$

$\sf{2x - x = 2 + 1}$

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$\sf{x = 3}$

$\rm{x + 1 , \: 3x ,\: 4x + 2}$ and so 5th term is

$\sf \underline \red{4 \: 9 \: 14}$

Answer 2

Given,

(x + 1), 3x and (4x + 2) are first three terms of an AP

a = x + 1 , a2 = 3x and a3= 4x + 2

a2 - a = a3 - a2

=> 3x - (x + 1) = (4x + 2) - 3x

=> 3x - x - 1 = 4x - 3x + 2

=> 2x - 1 = x + 2

=> 2x - x = 2 + 1

=> x = 3

Thus, x = 3

Then,

First-term = x + 1 = 3 + 1 = 4

Second term = 3x = 3(3) = 9

Third term = 4x + 2 = 4(3) + 2 = 14

Common difference = 5

Hence,

Fifth term = 14 + 10 = 24