Geometric Sequences

Master geometric sequences! Identify patterns, calculate common ratios, and write formulas.

Define the parts of the equation Given the explicit formula for a geometric sequence, define an, a1, r, and n. value of the nth term the first term common ratio (or multiplier) the number of terms Label the parts Label the common ratio and the first term in the following example. first term common ratio Geometric or Not? Sort the sequences into their proper categories Geometric Sequence 1, -4, 16, -64, ... -2, 4, -8, 16, ... Not Geometric -2, -4, -12, -48, ... Find the common ratio Match the sequence with the correct common ratio -3, 15, -75, 275, ... r = -5 38880, 6480, 1080, 180, ... r = 1 1250, -250, 50, -10, ... r = -1 -1, -6, -36, -216, ... r = 6 -2, -1, -1 -1 ... r = 1 2.5, 5, 10, 20, ... r = 2 Given the table below, find a1, r, and the 10th term. a1 = 2 r = -2, a10 = -1024 a1 = 3, r = 3, a10 = 13,122 a1 = 2, r = 3, a10 = 39,366 a1 = 2, r = 3, a10 = 118,098 Find the components of the Geometric Sequence Given the sequence below, find the explicit formula and the 12th term.3, 6, 12, 24, ... Given the explicit formula below, find the 9th term:an = 2(3)n - 1 13,122 39,366 54 4,374 Find the 12th term Given the explicit formula below, find the 12th term:an = (-3)n - 1 Write the recursive formula for the sequence: 4, 8, 16, 32,... a1=4 an = an-1 +2 a1=2an=an-1 +4 a1=4an=an-1 (2) a1=2an=an-1 (4) Write the explicit formula given the recursiveformula: a1=5 an = an-1(4) an=5(5)n-1 an=4(5)n-1 an=4(4)n-1 an=5(4)n-1 Write the first 4 terms: an=3(2)n-1 3, 6, 12, 24 2, 6, 18, 54 6, 12, 24, 48 6, 18, 54, 162