Question

Explain what it means for a sequence to be arithmetic and what it means for a sequence to be geometric. Give examples and highlight different representations as needed. Provide clear and complete descriptions of the underlying nature of each type of sequence.

Answer 1

Explanation:

when it says a sequence is arithmetic, it means that is has a common difference and come in the form a+(n-1)d, where a is the first term of the sequence, n is the number of terms and d is the common difference (the difference between each term.

example: 6, 3, 0, -3, -6

the common difference is 3, therefore its form is 6+(n-1)(-3) = 9-3n

if u wanted to find the 7th term in the sequence (
`a_7`), you'd put 7 in place of n in the equation.

geometric sequences have common ratios and come in the form ar^n-1

where a is the first term, r is the common ratio (basically the common difference but in the form of a fraction) and n is the number of terms.