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shepuryov [24]
3 years ago
5

In two or more complete sentences, explain whether the sequence is finite or infinite. Describe the pattern in the sequence if i

t exists, and if possible find the seventh term.
2a, 2a2b, 2a3b2, 2a4b3. . .
Mathematics
1 answer:
Ray Of Light [21]3 years ago
7 0

Answer:

Infinite sequence with terms t_{n+1}=t_n\cdot ab or t_{n+1}=2a\cdot (ab)^n=2a^{n+1}b^n.

t_7=2a^7b^6.

Step-by-step explanation:

Consider the pattern

2a,\ 2a^2b,\ 2a^3b^2,\ 2a^4b^3,\ ...

First term of this pattern is

t_1=2a,

second -

t_2=t_1\cdot ab,

third -

t_3=t_2\cdot ab,

fourth -

t_4=t_3\cdot ab,

fifth -

t_5=t_4\cdot ab=2a^4b^3\cdot ab=2a^5b^4,

sixth -

t_6=t_5\cdot ab=2a^5b^4\cdot ab=2a^6b^5,

seventh -

t_7=t_6\cdot ab=2a^6b^5\cdot ab=2a^7b^6.

This equence is infinite and each next term is obtained from the previous multiplying by ab.

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