Question

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

Answer 1

The nth term will be:

• 
  `a_(93)=-925`

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`