Question

NO LINKS!!!!

Answer 1

9514 1404 393

Answer:

  a. 12, 16, 20, 24; t(n)=4n

  b. 16, 32, 64, 128; t(n)=2·2^n

Step-by-step explanation:

a. The difference of the given terms is 8-4=4, so the arithmetic sequence has a first term of 4 and a common difference of 4. The general term has the formula ...

  t(n) = t(1) +d(n -1)

  t(n) = 4 +4(n -1) . . . . . with t(1) and d filled in

  t(n) = 4n . . . . . . . . . . simplified

This formula can be considered to be the generator of the sequence. For values of n from 3 to 6, the next four terms are ...

  t(3) = 12; t(4) =16; t(5) = 20, t(6) = 24

A table and graph are shown in the first attachment.

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b. The ratio of the given terms is 8/4 = 2, so the geometric sequence has a first term of 4 and a common ratio of 2. The general term has the formula ...

  t(n) = t(1)·r^(n-1)

  t(n) = 4·2^(n-1) . . . . . . . with t(1) and r filled in

  t(n) = 2·2^n . . . . . . . . simplified

This formula can be considered to be the generator of the sequence. For values of n from 3 to 6, the next four terms are ...

  t(3) = 16; t(4) = 32; t(5) = 64; t(6) = 128

A table and graph are shown in the second attachment.