Question

for the sequence -http://i.imgur.com/8LzC1jD.png
find first 5 terms
find the sum of 1st 25 terms
why is it a arithmetic sequence?

Answer 1

For the first 5 terms, substitute n = 1 (for the first), n = 2 (for the second), and so on to find them. :)

Answer 2

The value gotten for A(n) then equals the term.

Answer 3

so i got 9 13 17 21 25

Answer 4

Yes, that's correct!

Answer 5

okay what about 2?

Answer 6

Now the formula for the sum of an arithmetic progression is: \[S _{n} = \frac{ n }{ 2 }(2a + (n-1)d)\]where
s = sum of progression
n = number of terms
a = value of first term
d = difference between 2 terms

Answer 7

this one is confusing to me i don't get it

Answer 8

Therefore \[S _{25} = \frac{ 25 }{ 2 }(2(9) + (25 - 1)(13 - 9))\]

Answer 9

a = the value of this first term, in this case 9.
d = the difference between two of the terms, in this case (13 - 9) or (17 - 13) or (21 - 17), all of which equal 4.
This is also the reason that this is an arithmetic sequence, because the difference between each term is constant.

Answer 10

Okay i understand it's a arithmetic sequence now because the change is constant but i still cant figure out the 2nd one

Answer 11

wait i got 1425 is that right?

Answer 12

Yep, that's correct!

Answer 13

Ok ty!

Answer 14

You're welcome!