Introduction to Sequence

Which formula is used to find the explicit equation for geometric sequences?

• a_n = a_n-1 + d

• a_n = a_n-1 * r

• a_n = a₁ + d(n-1)

• a_n = a₁ * r^n-1

Given the sequence: 125, 25, 5, .... Write the explicit rule:

• a_n = (125)(1/5)^(n-1)

• a_n = 625(1/5)^(n-1)

• a_n = 625(5)⁽ⁿ⁾

• a_n = 125 + 5n

Given the sequence: 25, 21, 17, 13,... Write the explicit equation that models the sequence.

• a_n = 29-4(n-1)

• a_n = 4+25(n-1)

• a_n = 25-4(n-1)

• a_n = 4n + 25

What is the common ratio in this sequence?

• 1/2

• 2

• 12

• 24

The first term in a geometric sequence is 160 and the common ratio is 1/2.  What is the 7th term given the equation a_n = a₁ (r)^n-1

• 5

• 2.5

• 10

• 1.25

The graph of an arithmetic sequence is ​ ​ (a)   and the graph of a geometric sequence is ​ (b)   .

• linear

• exponential

-21, -16, -11, -6, ...

Is this sequence arithmetic, geometric, or neither?

• arithmetic (common difference d = 5)

• geometric (common ratio r = 5)

• neither (no common difference OR common ratio) neither (no common difference OR common ratio)

The explicit rule for the given graph is...