Question

3 + x, 9 + 3x, 13 + 4x, ... is an arithmetic sequence for some real number x.

Answer 1

Answer:

x = -2

Step-by-step explanation:

An arithmetic sequence is one where the difference between any two consecutive terms in the sequence is constant.

For any arithmetic sequence the general formula is as follow

$a_{n} = a_{1} + (n - 1)d$

where

$a_{n}$ is the nth arithmetic value

$a_{1}$ is the initial arithmetic value

$n$ is the nth term

$d$ is the difference is consecutive arithmetic values

To find the value of $x$ we form a number of simultaneous equations

$a_{1} = 3 + x\\ a_{2} = (3 + x) + 1 d\\ a_{3} = (3 + x) + 2 d$

from the given information we also know that

$a_{2} = 9 + 3 x\\ a_{3} = 13 + 4x$

Solving these equations simultaneous we find the value of x to be

$x = -2$