swag asked in Science & MathematicsMathematics · 5 months ago

# Please question number 8 Fast?

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• 5 months ago

The nth term of that sequence could be:

-(31/120)n^4 + (77/24)n^3 - (335/24)n^2 + (595/24)n - (887/60)

In that case:

Term 6 is -31/3

Term 7 is -45

Term 8 is -501/4

• 5 months ago

Find a possible formula for the nth term of a sequence whose first five terms are given,

and use this formula to write the next three terms of the sequence.

-1, 1/2, -1/3, 1/4, -1/5, ...

an = (-1)^n/n

The next three terms of the sequence: 1/6, -1/7, 1/8, ...

• geezer
Lv 7
5 months ago

SERIOUSLY .. You can't do the easiest one there ?

• 5 months ago

As for what the formula is, the numerators are a geometric sequence starting with -1 and a common ratio of -1, or:

-1 * (-1)^(n - 1)

Since we have two numbers of the same base we can add the exponents to simplify to get:

(-1)^n

Then the denominator is an arithmetic sequence starting with 1 and increasing by 1:

1 + 1(n - 1)

Which simplifies to:

1 + n - 1

n

So combining them, your expression for the "n"th term of this sequence is:

(-1)^n / n