Question

The first difference of a sequence is the arithmetic sequence 2, 4, 6, 8, 10.... find the first six terms of the original sequence in each of the following cases letter
a. The first term of the original sequence is 2. b. The sum of the first two terms in the original sequence is 12
C. The fifth term in the original sequence is 36.

Answer 1

Answer:

  a.  2, 4, 8, 14, 22, 32

  b.  5, 7, 11, 17, 25, 35

  c.  16, 18, 22, 28, 36, 46

Step-by-step explanation:

a. Add each of the first differences to the previous term.

  first term: 2 . . . (given)

  second term: 2 +2 = 4

  third term: 4 +4 = 8

  fourth term: 8 +6 = 14

  fifth term: 14 +8 = 22

  sixth term: 22 +10 = 32

The first 6 terms of the sequence are 2, 4, 8, 14, 22, 32.

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b. If the first term is n, then the second term is n+2, and their sum is ...

  n +(n+2) = 12

  n = (12 -2)/2 = 5 . . . . solve for n

The first 6 terms of the sequence are 5, 7, 11, 17, 25, 35.

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c. You may have noticed from the above that the 5th term is 20 more than the first term. For this sequence, the first term will be 36 -20 = 16.

The first 6 terms of the sequence are 16, 18, 22, 28, 36, 46.