Describe the pattern of the sequence.$-1,\ -8,\ -27,\ -64,\ ...$−1, −8, −27, −64, ...Responsesthe number of each term is squared and the opposite is appliedthe number of each term is squared and the opposite is appliedthe number of each term is cubed and the opposite is appliedthe number of each term is cubed and the opposite is appliedQuestion 2Find the next term.$a_5=$a5= Question 3Write the rule for the $n^{th}$nth term.$a_n=$an=
Question
Describe the pattern of the sequence.−1, −8, −27, −64, ...Responsesthe number of each term is squared and the opposite is appliedthe number of each term is squared and the opposite is appliedthe number of each term is cubed and the opposite is appliedthe number of each term is cubed and the opposite is appliedQuestion 2Find the next term.a5= Question 3Write the rule for the nth term.an=
Solution
The pattern of the sequence is that each term is the negative cube of a natural number.
For the first term, 1 is cubed and then negated to get -1. For the second term, 2 is cubed and then negated to get -8. For the third term, 3 is cubed and then negated to get -27. For the fourth term, 4 is cubed and then negated to get -64.
So, to find the next term, we cube the next natural number, 5, and then negate it.
The rule for the nth term is that it is the negative cube of n.
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