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nth Term of an AP

x +1, 3 x and...

Question

$(x + 1), 3 x a n d (4 x + 2)$ are first three terms of an AP. Find its $5^{t h}$ term.

A

14

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B

19

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C

24

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D

28

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Solution

The correct option is C
24

For a set of numbers to be in AP, the difference between any two consecutive terms should be constant.

If $a_{1}, a_{2}, a_{3}$ are in AP, then

$a_{2} - a_{1} = a_{3} - a_{2}$ = d

where 'd' is the common difference.

Given, $(x + 1), 3 x, (4 x + 2)$ are in AP

$∴$ $3 x - (x + 1) = (4 x + 2) - 3 x$

$\Rightarrow$ $x = 3$

$∴$ $a_{1}$ = $(x + 1)$ = 3+1 = 4

$a_{2}$ = $3 x$ = 9

d = $a_{2} - a_{1}$ = 9 - 4 = 5

The formula to find the $n^{t h}$ term of an arithmetic progression is $t_{n} = a_{1} + (n - 1) d$

where,

' $a_{1}$ ' is the first term,

'd' is the common difference,

'n' is the no. of terms,

' $t_{n}$ ' is the $n^{t h}$ term.

Substituting the values, we get

$t_{5} = 4 + 4 (5) = 24$

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(x + 1), 3 x

(4 x + 2)

are the first three terms of an A.P., then the value of

5^{t h}

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