Question

5.Jackie deposited $5 into a checking account in February. For each month following, the deposit
amount was doubled. How much money was deposited in the checking account in the month of
August? (1 point) This is an geometric sequence because..?
7.A major US city reports a 12% increase in decoration sales during the yearly holiday season. If decoration sales were 8 million in 1998, how much did the city report in total decoration sales by the end of 2004? (1 point). This is an geometric series because..?
(explain in complete sentences.)

Answer 1

5 + 2 x 5 + 2^2 5 + 2^3 5 + 2^4 5 + 2^5 5+ 2^6 5=
5( 1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6)=
\[
5 \frac { 1- 2^7}{1-2}= 5 (2^7-1)= 635
\]
This is the total for all month up to an including August.
In August, the deposit was 5 (2^6)=320

Answer 2

so would i say its a geometric sequence because..

Answer 3

Every deposit is 2 times the previous one. That is a geometric series
with first term 5 and r = 2. Meaning that
\[
a_0=5\\
a_n= 2 a_{n-1}
\]

Answer 4

thanks and do uk wat the second one wld be in other words why is it a geometric series

Answer 5

For the second one
\[
a_0= 8\\
a_1= 8 ( 1.12)\\
a_2= 8(1.12)^2\\

a_n= 8(1.12)^n

\]
You need to find
\[
a_0+ a_1 + a_2 + a_3 + a_4 + a_5 + a_6=80.7121 \text { million}

\]

Answer 6

huh?

Answer 7

\[
8\sum_{k=0}^6 (1.12)^k= 8 \frac { 1- (1.12)^{7}}{1-1.12} =80.7121
\]

Answer 8

so wat would be my explanation to why its a geometric series

Answer 9

\[
a_0= 8\\
a_1= 8 ( 1.12)\\
a_2= 8(1.12)^2\\

a_n= 8(1.12)^n
\]

Answer 10

Every year is 1.12 times the previous year