How to find and write the first four terms of the sequences below with the given general term? (1) a_n=(-1)^(n+1)(n+4) (2) a_n=(-1)^(n-1)n^2

2 Answers
Jun 21, 2018

For any sequence, the first term a1 is when n=1, the second term a2 is when n=2 and so on.
For your first sequence a_1=(-1)^(1+1)(1+4)=5
a_2=(-1)^(2+1)(2+4)=-6
continue for each term

Explanation:

Replace n by the whole number indicating the term you are calculating. A sequence is a list of terms in a specific order, the order is given by n, the value is given when you substitute n into the formula.

Jun 21, 2018

(1) +5,-6,+7,-8
(2) +1,-4,+9,-16

Explanation:

(1)
a_n=(-1)^(n+1) (n+4)

The first 4 terms of the sequence with general term (n+4) are: 5,6,7,8

(-1)^(n+1) simply means that odd terms will be positive and even terms will be negative.

Hence, a_(n=1->4)=(-1)^(n+1) (n+4) = +5,-6,+7,-8

(2)
a_n=(-1)^(n-1) n^2

The first 4 terms of the sequence with general term n^2 are: 1,4,9,16

(-1)^(n-1) also means that odd terms will be positive and even terms will be negative. [Since, (-1)^0 = 1]

Hence, a_(n=1->4)=(-1)^(n-1) n^2 = +1,-4,+9,-16