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High School Mathematics - 2
3.11 Find the First Four Terms of the Sequence

Find the first four terms and state whether the sequence is arithmetic, geometric, or neither.
  1. an = 3n + 2
    To find the first four terms, in a row, replace n with 1, 2, 3 and 4
    3n + 2 = 3(1) + 2 = 3 + 2 = 5
    3n + 2 = 3(2) + 2 = 6 + 2 = 8
    3n + 2 = 3(3) + 2 = 9 + 2 = 11
    3n + 2 = 3(4) + 2 = 12 + 2 = 14
    Answer: The first four terms of the sequence are 5, 8, 11, 14. This sequence is arithmetic with common difference of d = 3
  2. an = n2 + 1
    substituting n = 1,2,3,4
    n2 + 1 = 12 + 1 = 1 + 1 = 2
    n2 + 1 = 22 + 1 = 4 + 1 = 5
    n2 + 1 = 32 + 1 = 9 + 1 = 10
    n2 + 1 = 42 + 1 = 16 + 1 = 17
    Answer: The first four terms of the sequence are 2, 5, 10, 17. The sequence is neither arithmetic nor geometric.
  3. an = 3.2n
    substituting n = 1,2,3,4
    3.2n = 3.21 = 3 x 2 = 6
    3.2n = 3.22 = 3 x 4 = 12
    3.2n = 3.23 = 3 x 8 = 24
    3.2n = 3.24 = 3 x 16 = 48
    Answer: The first four terms of the sequence are 6, 12, 24, 48. The sequence is geometric with r = 2.

Directions: Answer the following questions. Also write at least 5 examples of your own.
Q 1: Find the first four terms of the sequence: 2n
1,3,5,7
2,4,8,16
2,4,6,8

Q 2: Find the first four terms of the sequence: (n+1)/n
1/2,2/3,3/4,4/5
1/1,2/2,3/3,4/4
2, 3/2, 4/3, 5/4

Q 3: Find the first four terms of the sequence: 3n/3!
3,9/2,9/2,27/8
2/9,3/9,4/9,7/9
3,9/2,9/2,27/9

Q 4: Find the first four terms of the sequence: 2/3
2/3, 2/3, 2/3, 2/3
1,1,1,1
1,2/3,1,2/3

Q 5: Find the first four terms of the sequence: (-2)n
-2,4,-8,16
-2,-4,-8,-16
2,-4,8,-16

Q 6: Find the first five terms of the sequence: 2n + 1
3,5,7,9,11
1,3,5,7,9
2,6,8,10,11

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!


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