CP Algebra 2
Sec. 10-3 Geometric Sequences
Name_______________________
Warm up
1. Find a11 for 5. 10, 20 , …
2. Write an equation for the nth term of
32768, 4096, 512, 64…
3. Find the geometric means for 51, ______, _________, _________, 3334611
Given the explicit formula for a geometric sequence find the first five terms and write the
recursive formula.
4.
5.
an = −2.5(4) n −1
an = 1000(0.5) n −1
Given two terms in a geometric sequence find the 8th term and the recursive formula.
6.
a4 =−12 and a5 =−6
7.
a5 =768 and a2 =12
Given the recursive formula for a geometric sequence find the common ratio, the first five
terms, and the explicit formula.
8.
a1 = 1
an = an −1 ⋅ −2
9.
a1 = 3
an = an −1 ⋅ 4
Geometric Series
The square below is 1 unit x 1 unit.
Divided the square into fourths. Shade the 3rd quadrant.
Label the dimensions of the shaded square.
Divide the 1st quadrant square into fourths. Shade the 3rd quadrant. Label the dimensions of the
shaded square.
Repeat 3 more times.
Record the area for each stage.
Stage
Area of
shaded
square
0
1
2
3
4
5
n
Find the sum of the squares for the first 5 stages. Use the summation formula for a geometric
a1 (1 − r n )
series. Sn =
.
1− r
∞
1.
Write each series using sigma notation.
a.
625 + 125 + 25 + 5 + 1
2.
Write each series in expanded form and calculate the sum.
b.
6
a.
∑2
2401 + 343 +49 + 7
5
k
b.
k =1
∑ 3 (2 )
1
k −1
k =1
3.
During a week-long sale, a store reduced its prices on sale items by 10% each day. A coat
that was priced $80 on the first day of the sale was sold on the fourth day. At what price
was the coat sold?
4.
A champion bullfrog leaps in a geometric sequence where each succeeding jump is
5.
Find a1 for each geometric series described.
a.
Sn = –342, an = –512, r = –2
2
of
3
the previous jump. If the frog’s first leap is 27 feet, find the distance the frog has covered
after 5 leaps.
b.
Sn = 1295, r = 6, n = 4
Homework….Page 678 #47 -54 and handout and Problems 1 – 3 below.
1.
Write the recursive formulas for the following geometric sequences.
a.
512, 256, 128, 64 …
t1 =
tn =
b.
768, 384, 192, 96, …
t1 =
tn =
c.
8, 32, 128, 512, …
t1 =
tn =
2.
Find the first 5 terms of each geometric sequence. If necessary, round to the
nearest tenth.
⎧t1 = 4
a. ⎨
⎩t n = t n −1 • 3
3.
⎧u1 = 2.1
b. ⎨
⎩un = un −1 • 2
Write the recursive and function formulas for each of the geometric sequences.
a.
0.1, 1, 10, 100, 1000, …
b. 6, 36, 216, 1296, …