Formulas for Arithmetic and Geometric Sequences
Check For Understanding – Formulas for Arithmetic and Geometric Sequences Directions: Complete without notes and by yourself to determine whether you have mastered this objective. 1) In a geometric sequences, a1 = 1 and a5 = 81. Write an explicit formula to find the nth term of this sequence.
2) Now write a recursive formula for the sequence in question #1.
3) What is the common ratio of the geometric sequence below? 8, 2, ½ , ,
4) The first five terms of an arithmetic sequence are seen below. Write an explicit AND a recursive formula to represent this sequence: 3, 8, 13, 18, 23
5) Find the first five terms of the sequence given by the formula a1 = 4 and an = (an – 1)∙3
6) Find the explicit formula for the following sequence: 3, -6, 12, -24, 48…..
7) Is the following a sequence or a series? Geometric or arithmetic? Explain your answer. 1, 4, 16, 64, 256 8) Let
{
}
a. Identify b. Is this sequence arithmetic or geometric? Why? c. What is the common difference or ratio?
Answer Key: 1) an = 3n-1 2) an = 3 * (an-1) 3) ¼ 4) Explicit: an = 3 + 5(n-1) Recursive: an = an-1 + 5 5) 4, 12, 36, 108, 324 6) an = 3 * (-2)n-1 7) Sequence because it is a list of numbers, not a sum. Geometric because you are multiplying each time .
8) a: -16 b: Geometric – multiplying c: -2
2) Now write a recursive formula for the sequence in question #1.
3) What is the common ratio of the geometric sequence below? 8, 2, ½ , ,
4) The first five terms of an arithmetic sequence are seen below. Write an explicit AND a recursive formula to represent this sequence: 3, 8, 13, 18, 23
5) Find the first five terms of the sequence given by the formula a1 = 4 and an = (an – 1)∙3
6) Find the explicit formula for the following sequence: 3, -6, 12, -24, 48…..
7) Is the following a sequence or a series? Geometric or arithmetic? Explain your answer. 1, 4, 16, 64, 256 8) Let
{
}
a. Identify b. Is this sequence arithmetic or geometric? Why? c. What is the common difference or ratio?
Answer Key: 1) an = 3n-1 2) an = 3 * (an-1) 3) ¼ 4) Explicit: an = 3 + 5(n-1) Recursive: an = an-1 + 5 5) 4, 12, 36, 108, 324 6) an = 3 * (-2)n-1 7) Sequence because it is a list of numbers, not a sum. Geometric because you are multiplying each time .
8) a: -16 b: Geometric – multiplying c: -2
