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In two or more complete sentences, explain whether the sequence is finite or infinite. Describe the pattern in the sequence if it exists, and if possible find the sixth term. 3a, 3a2b, 3a3b2, 3a4b3. . .

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merlynthewhizz
The sequence is given as follow
[tex]3a[/tex],[tex]3 a^{2}b,3 a^{3} b^{2} , 3 a^{4} b^{3} [/tex]

When finding the pattern of a sequence, we can try to work out whether there is a common difference or a common ratio between each term. We try by finding a common ratio

[tex] \frac{3 a^{2}b }{3a} =ab[/tex]
[tex] \frac{3 a^{3 b^{2} } }{3 a^{2}b }=ab [/tex]
[tex] \frac{3 a^{4} b^{3} }{3 a^{3} b^{2} }=ab [/tex]

The term to term rule is multiplied by [tex]ab[/tex]

The [tex] 5^{th} [/tex] term is given [tex]3 a ^{4} b^{3} [/tex]×[tex]ab=3 a^{5} b^{4} [/tex]

The [tex] 6^{th} [/tex] term is given by [tex]3 a^{5} b^{4} [/tex]×[tex]ab=3 a^{6} b^{5} [/tex]

Answer:

This sequence is infinite because it is never ending, due to the... which tells us that this sequence goes on forever. The pattern in this sequence is 3a(ab)^n-1 and the sixth term is 3a^6b^5.

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