Question

8. A geometric sequence has a4=4 and a5=7 . What is a1 ?

Answer 1

Can you alos help me with this? @jim_thompson5910 I understand how to find partial sums but i dont know how to find a1

Answer 2

what is the common ratio here? are you able to find it?

Answer 3

its 1.75

Answer 4

correct, so r = 1.75

Answer 5

the nth term of a geometric sequence is

\[\Large a_{n} = a_1*(r)^{n-1}\]

Answer 6

we're given \[\Large a_4 = 4\]
so n = 4 and \(\Large a_n = 4\)

\[\Large a_{n} = a_1*(r)^{n-1}\]
\[\Large a_{4} = a_1*(1.75)^{4-1}\]
\[\Large 4 = a_1*(1.75)^{4-1}\]

are you able to isolate \(\Large a_1\) ?

Answer 7

yes

Answer 8

would a1= 1.3593

Answer 9

I think you divided in the wrong order

Answer 10

I'm getting 0.7463556851312

Answer 11

if you kept everyhing as a fraction, then

\[\Large n = 4\]
\[\Large a_n = 4\]
\[\Large r = \frac{7}{4}\]


would lead to

\[\Large a_1 = \frac{256}{343}\]

Notice how
\[\Large \frac{256}{343} \approx 0.7463556851312\]