nth Term
Find the 3rd term of the geometric sequence given
a2 = 6 and r = -5
a3 = -30
Find the common ratio given the first four terms of the geometric sequence 7, 14, 28, 56,...
r = 2
Write the recursive formula of the sequence:
52, 26, 13,...
an = an-1 x (1/2)
The population of mice in a barn doubles every day. There are initially 2 mice in the barn on day one. How many mice are in the barn on day nine?
512 mice
Geometric Sequences resemble this type of function when graphed.
Exponential
Find the 7th term of the geometric sequence given
a1 = 1 and r = 4.
a7 = 4,096
Find the common ratio given the explicit formula for a geometric sequence.
an = -75(-14)n-1
r = -14
The explicit formula for the nth term of a sequence is an = 10(4)n-1
Write the recursive formula for the same sequence.
an = an-1 x 4
A female cat gives birth to five female kittens (a1=5). As each of these kittens grows up, they also have five female kittens of their own. If this pattern of reproduction continues, how many female kittens will be born in the 4th generation (a4)?
625 female kittens
Find the first four terms of the geometric sequence for which a1 = 6 and r = 2
6, 12, 24, 48
Find the 8th term of the geometric sequence given
a2 = -6, a3 = -12, and a4 = - 24
a8 = -384
DAILY DOUBLE
Find the common ratio of the geometric sequence given a4 = 81 and a2 = 9
r = 3
Write the explicit formula for the sequence -12, -18, -27, -40.5,..
an = -12(1.5)n-1
Jack plants a bean sprout that is two centimeters tall after the first day. Every day the plant triples in size. How tall is the plant after the 16th day?
28,697,814 cm or 286,978.14 m
Find the first four terms of the geometric sequence
an = -7(3)n-1
-7, -21, -63, -189
DAILY DOUBLE
The first three terms of a geometric sequence are 0.8, 0.4, 0.2,.. Find the 6th term of the geometric sequence.
0.025 or 1/40
Find the common ratio of the geometric sequence -0.5, 2, -8, 32,..
r = -4
Two terms of a geometric sequence are
a1 = -4 and a2 = -12.
Write the recursive formula for the nth term.
an = an-1 x 3
Brianna puts five cents into a special investment account. Her money grows by a common ratio of 1.2 per day. How much money will be in her account after 21 days?
$1.92
Find the first four terms of the geometric sequence for which a4 = 1216 and r = 4.
Given a1 = -1,500 and r = -0.1 in a geometric sequence, find a10.
a10 = 0.0000015
Find the common ratio of the geometric sequence 1000, 250, 62.5, 15.625
r = 1/4
Write the explicit formula for the nth term of the geometric sequence with a2 = -84 and a3 = 63
an = 112(-3/4)n-1
A small town is planning to plant trees along a new road. The first year, they plant 2 trees. Each subsequent year, they plan to plant 3 times the number of trees they planted the previous year.
How many trees will they have planted in TOTAL after 5 years?
2 + 6 + 18 + 54 + 162 = 242 trees
Two terms of a geometric sequence are
a2 = 9 and a4 = 576.
Find r for this sequence.
r = 8