Question

in each of the following, list three terms that continue the arithmetic or geometric sequences. identify t
a. 1, 8, 15, 22, 29
b. 2, 6, 18, 54, 162
c. 15, 22, 29, 36, 43

a. the next three terms of 1, 8, 15, 22, 29 are \\(\square\\), \\(\square\\), and \\(\square\\). (use ascending order.)
is the sequence arithmetic or geometric?
\\(\bigcirc\\) a. geometric
\\(\bigcirc\\) b. arithmetic

b. the next three terms of 2, 6, 18, 54, 162 are \\(\square\\), \\(\square\\), and \\(\square\\). (use ascending order.)
is the sequence arithmetic or geometric?
\\(\bigcirc\\) a. geometric
\\(\bigcirc\\) b. arithmetic

c. the next three terms of 15, 22, 29, 36, 43 are \\(\square\\), \\(\square\\), and \\(\square\\). (use ascending order.)
is the sequence arithmetic or geometric?
\\(\bigcirc\\) a. arithmetic
\\(\bigcirc\\) b. geometric

Explanation:

Part a

Step1: Identify sequence type

Check difference: \(8 - 1 = 7\), \(15 - 8 = 7\), \(22 - 15 = 7\), \(29 - 22 = 7\). Common difference \(d = 7\), so arithmetic.

Step2: Find next terms

Last term is \(29\). Next term: \(29 + 7 = 36\); then \(36 + 7 = 43\); then \(43 + 7 = 50\).

Step1: Identify sequence type

Check ratio: \(\frac{6}{2} = 3\), \(\frac{18}{6} = 3\), \(\frac{54}{18} = 3\), \(\frac{162}{54} = 3\). Common ratio \(r = 3\), so geometric.

Step2: Find next terms

Last term is \(162\). Next term: \(162\times3 = 486\); then \(486\times3 = 1458\); then \(1458\times3 = 4374\).

Step1: Identify sequence type

Check difference: \(22 - 15 = 7\), \(29 - 22 = 7\), \(36 - 29 = 7\), \(43 - 36 = 7\). Common difference \(d = 7\), so arithmetic.

Step2: Find next terms

Last term is \(43\). Next term: \(43 + 7 = 50\); then \(50 + 7 = 57\); then \(57 + 7 = 64\).

Answer:

Next three terms: \(36\), \(43\), \(50\); Sequence type: B. Arithmetic

Part b