Question

Find the 93rd term of the arithmetic sequence -5, -15, -25, ...−5,−15,−25,...

Answer 1

Answer:

The nth term will be:

• $a_{93}=-925$

Step-by-step explanation:

Given the sequence

-5, -15, -25, ...

An arithmetic sequence has a constant difference 'd' and is defined by  

$a_n=a_1+\left(n-1\right)d$

computing the differences of all the adjacent terms

$-15-\left(-5\right)=-10,\:\quad \:-25-\left(-15\right)=-10$

The difference between all the adjacent terms is the same and equal to

$d=-10$

The first element of the sequence is:

$a_1=-5$

Thus, the nth term will be:

$a_n=a_1+\left(n-1\right)d$

substituting the values $d=-10$; $a_1=-5$

$a_n=-10\left(n-1\right)-5$

$a_n=-10n+5$

Plug in n = 93 to determine the nth term

$a_{93}=-10\left(93\right)+5$

$a_{93}=-930+5$

$a_{93}=-925$

Therefore, the nth term will be:

• $a_{93}=-925$