Question

Can someone please help me! I will fan+medal
Find the sum of the first six terms of the geometric sequence for which a2=0.7 and a3=0.49

Answer 1

what is the value of r?

Answer 2

0.7

Answer 3

so what is the value of a1, a4, a5, a6?

Answer 4

well we don't even need all of the terms

Answer 5

a1=0.1
a4=3.43
a5=24.01
a6=168.07

Answer 6

you're multiplying by 0.7 not 7. the numbers should be getting smaller after a3. im trying to find that one formula

Answer 7

but to get to 0.7 you must multiply 0.1 times 7 and to get to 0.49 you must multiply 0.7 to 0.7

Answer 8

if you see 0.7 times 0.7=0.49

Answer 9

ok I found it. \(\huge S_n=a_1(\frac{{1-r}^n}{1-r})\)

Answer 10

ok first thing's first, to get a1, we have to divide a2 by 0.7 because we're working backwards.

Answer 11

mhmm

Answer 12

thats 0.1

Answer 13

if a1 = 0.1 and the ratio = 0.7
a2 would be 0.07

if a1 = 1 and the ratio = 0.7
a2 would be 0.7

Answer 14

oh okay

Answer 15

For reference, 0.7/0.7 = \(a_1\) = 1

Answer 16

yeah makes sense

Answer 17

so where were we \(\huge S_n=a_1(\frac{{1-r}^n}{1-r})\)
\(\huge S_n=1(\frac{{1-0.7}^6}{1-0.7})=\frac{0.3^6}{0.3}\)

Answer 18

umm i got 0.00243

Answer 19

same I don't know if that makes sense

Answer 20

1+0.7+0.49+... should be at least 1

Answer 21

but the way i did it before, the way that you thought was wrong i got 196.8

Answer 22

That's definitely wrong.

1, 0.7, 0.49, 0.343, 0.2401, 0.16807 is the actual series assuming r = 0.7

Answer 23

hmm so lost

Answer 24

here, if \(\large a_2=0.7 \)
\(\large a_3=0.49 \)

That means the common ratio is 0.7. That also means that \(\large a_1=1\) and \(\large a_4=0.343\)

Answer 25

so whats the answer?

Answer 26

1 + 0.7 + 0.49 + 0.343 + 0.2401 + 0.16807

Answer 27

I'll try it again with one of the formulas in a sec

Answer 28

oh wow I'm an absolute idiot

Answer 29

?

Answer 30

\(\huge S_n=a_1(\frac{{1-(r}^n)}{1-r})\)\(\large r=0.7, n =6\)

\[\large S_n=(\frac{{1-(r}^n)}{1-r})=(\frac{{1-(0.7}^6)}{1-0.7})=\frac{1-0.117649}{0.3}= \frac{0.882351}{0.3}=2.94117\]

Answer 31

2.94117

Answer 32

thats the final answer?

Answer 33

yeah. I did the math too, google agrees
1 + 0.7 + 0.49 + 0.343 + 0.2401 + 0.16807 =2.94117

Answer 34

thanks so much!

Answer 35

sorry about getting caught up with something as stupid as an arithmetic mistake

Answer 36

its geometric :) and its okay

Answer 37

I can't tell if that's a joke or not :p
I meant the fact that I subtracted before raising the power. PEDMAS