Question

In the comments!

Answer 1

@hartnn This one is kind of similar to the last one but could you help me again?

Answer 2

what is the pattern you observed ?

the common difference is ?

Answer 3

937.50 to 875.00 is
62.5
875.00 to 812.50
62.5
812.50 to 750.00
62.5
750.00 to 687.50
62.5

Answer 4

There's typo in the question so I fixed it there lol.

Answer 5

yes, so common difference = d = -62.5
right ?

Answer 6

Yeah so my equation will be
1000-62.5n?

Answer 7

lets see

\(a_n = a_1 + (n-1)d \\ \quad = 937.5 + (n-1)(-62.5) \\ \quad = \)

correct!

Answer 8

So is my equation the explicit formula?

Answer 9

yes, explicit formula means in terms of x

implicit formula means in terms of next or previous terms...like for here,
\(a_n = a_{n-1} -62.5\)

Answer 10

What's the difference between an implicit and explicit formula?

Answer 11

explicit formula does not depend on previous or next terms
it only depends on 'n' , which is the index of the terms

implicit formula can depend on 'n' and previous or next terms

Answer 12

So how do I write an explicit formula for this?

Answer 13

1000-62.5n
is indeed the explicit formula
because it just depends on n

Answer 14

Oh okay just making sure!
In step one it says generalize in terms of n. What does that mean?

Answer 15

And for step 3
I think it is
-62.5n = -1000
n = 1000/62.5

Answer 16

i think generalize in terms of 'n' will give you 1000-62.5 n
which also happens to be the explicit formula

and for step 3
i think they are asking to isolate 'n' from
\(a_n = 1000 - 62.5 n\)

Answer 17

Okay and
step 3:
would I just subtract 1000 and then divide by -62.5 to get n by itself?

Answer 18

thats correct :)

Answer 19

Awesome!