Mathematics: Determine the arithmetic sequence if the fourth term is negative six and the eleventh term is negative thirty four

Determine the arithmetic sequence if the fourth

Ответ:

JadaaJayy

01.01.2022

Mathematics

An arithmetic sequence takes the form

$a_n=a_{n-1}+d$

where

is the common difference between terms. You can solve for a_n

in terms of any of the previous terms of the sequence:

$a_n=a_{n-1}+d\implies~a_n=a_{n-2}+2d\implies~a_n=a_{n-3}+3d\implies\cdots\implies~a_n=a_{n-k}+kd$

for some integer $1\le k\le n-1$

Continuing in this way, you know that the sequence can be defined explicitly in terms of the first term a_1

Given that the 4th term is a_4=-6

and the 11th term is $a_{11}=-34$ , you have the following system of equations.

$\begin{cases}-6=a_1+(4-1)d\\-34=a_1+(11-1)d\end{cases}$

Solving this system for the two unknowns yields a_1=6