Question

write an equation for each sequence below and determine the 8th term.
d) 7, 7.5, 7.75, 7.875...

Answer 1

7+ (0.5)^x

Answer 2

x begins from 0

Answer 3

x being the nth term?
but that doesn't work...
if x starts from 0
then that me ants the first term should be 8
not 7.

Answer 4

when x=0 then ans will be 8

Answer 5

see
modify it to
7 + (0.5)^(n-1)

Answer 6

nope

Answer 7

it still makes the first term 8 not 7.

Answer 8

8th term will be 7.9921875

Answer 9

trying to make an equation

Answer 10

nth term is 8 - (1/2)^(n-1),
and 8th term is 8 - (1/2)^(7) = 8-1/128 = 7 127/128.

Answer 11

that's what i got as well.
this is the equation my teacher came up with when i asked him
\[t _{n}=8-1/2^{n-1}\]

Answer 12

ye i got 7.992

Answer 13

yes this equation perfectally suit the series

Answer 14

okay. this is the right equation... i just don't get how he got to that.
he told me that \[t _{1}= 7\] \[t_{2}= 7 + 1/2 \] \[t_{3}= 7 + 1/2 + 1/2^{2}\]
and so on.
and then he got a =1/2, n=n-1, r=1/2
we know that a geometric sequence equation is represented by \[t_{n} = ar^{n-1}\]
therefore with that, he did
\[t_{n}= 7 + 1/2(1-1/2^{n-1})/1-1/2\]
\[=8-1/2^{n-1}\]