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

Sagot :

absor201

Answer:

The nth term will be:

  • [tex]a_{93}=-925[/tex]

Step-by-step explanation:

Given the sequence

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

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

[tex]a_n=a_1+\left(n-1\right)d[/tex]

computing the differences of all the adjacent terms

[tex]-15-\left(-5\right)=-10,\:\quad \:-25-\left(-15\right)=-10[/tex]

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

[tex]d=-10[/tex]

The first element of the sequence is:

[tex]a_1=-5[/tex]

Thus, the nth term will be:

[tex]a_n=a_1+\left(n-1\right)d[/tex]

substituting the values [tex]d=-10[/tex]; [tex]a_1=-5[/tex]

[tex]a_n=-10\left(n-1\right)-5[/tex]

[tex]a_n=-10n+5[/tex]

Plug in n = 93 to determine the nth term

[tex]a_{93}=-10\left(93\right)+5[/tex]

[tex]a_{93}=-930+5[/tex]

[tex]a_{93}=-925[/tex]

Therefore, the nth term will be:

  • [tex]a_{93}=-925[/tex]
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