Daily Check 1)Find the first 3 terms of the following sequence: 2)Write the formula for the following arithmetic sequence. -2, 1, 4, 7, 10

Algebra 1 Today’s Question: How is a geometric sequence like an exponential function?

Sequences and Series

Geometric Sequences In geometric sequences, you multiply by a common ratio each time. 1, 2, 4, 8, 16,... multiply by 2 27, 9, 3, 1, 1/3,... Divide by 3 which means multiply by 1/3

Geometric Sequences Find the 8 th term of the sequence: 2,6,18,… Determine the pattern: Multiply by 3 (known as the common ratio) Write the new sequence: 2,6,18,54,162,486,1458,4374 So the 8 th term is 4374.

Geometric Sequences Again, use a formula to find large numbers. a n = a 1 (r) n-1

Geometric Sequences Find the 10 th term of the sequence : 4,8,16,… a n = a 1 (r) n-1 a 1 = 4 r = 2 n = 10

Geometric Sequences a n = a 1 (r) n-1 a 10 = 4 (2) 10-1 a 10 = 4 (2) 9 a 10 = a 10 = 2048

Geometric Sequences Find the ninth term of a sequence if a 3 = 63 and r = -3 a 1 = ? n= 9 r = -3 a 9 = ? There are 2 unknowns so you must…

Geometric Sequences First find t 1. Use the sequences formula substituting t 3 in for t n. a 3 = 63 a 3 = a 1 (-3) = a 1 (-3) 2 63= a = a 1

Geometric Sequences Now that you know t 1, substitute again to find t n. a n = a 1 (r) n-1 a 9 = 7 (-3) 9-1 a 9 = 7 (-3) 8 a 9 = a 9 = 45927