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### High School Mathematics - 23.11 Find the First Four Terms of the Sequence

 Find the first four terms and state whether the sequence is arithmetic, geometric, or neither. 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 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. 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: 2n1,3,5,72,4,8,162,4,6,8 Q 2: Find the first four terms of the sequence: (n+1)/n1/2,2/3,3/4,4/51/1,2/2,3/3,4/42, 3/2, 4/3, 5/4 Q 3: Find the first four terms of the sequence: 3n/3!3,9/2,9/2,27/82/9,3/9,4/9,7/93,9/2,9/2,27/9 Q 4: Find the first four terms of the sequence: 2/32/3, 2/3, 2/3, 2/31,1,1,11,2/3,1,2/3 Q 5: Find the first four terms of the sequence: (-2)n-2,4,-8,16-2,-4,-8,-162,-4,8,-16 Q 6: Find the first five terms of the sequence: 2n + 13,5,7,9,111,3,5,7,92,6,8,10,11 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!

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