Day 3 Lesson 15 Geometric Sequences and Series

Determine whether each sequence is geometric or not.

Find the common ratio and the next term of each geometric sequence.

a) 2/3, 4, 24, 144, ...

r =​ (a)   ; a_{5 =}​​ (b)  

b) 9, -3, 1, -1/3, ...

r =​ (c)   ​ ; a_{5 =}​​ (d)  

What is the explicit formula of the geometric sequence,

$$2,\ \frac{1}{4},\ \frac{1}{32},\frac{1}{256},...?$$

Find the 7th term of the geometric sequence in which $$a_1=\frac{3}{8}$$ and $$r=\frac{1}{4}$$ .

Find the missing terms of the geometric sequence:

-3, ​ (a)   ​, (b)   , 648, ...

Find the first term of a geometric sequence whose second term is $$\frac{3}{4}$$ and the seventh term is $$-24$$ .

What is the value of k to make the sequence, $$-36,\ 6k,\ -9,\ ...,$$ geometric?

If a $$a_1=7,\ a_n=567,$$ and $$r=3,$$ find n.

What is the sum of the first 11 terms of the geometric sequence: $$3,\ -9,\ 27,\ -81,\ ...?$$

What is the partial sum of the geometric series, 2 + 10 + 50 + ... + 6250?