Question

Check my answers?

http://prntscr.com/d301oj

Answer 1

@phi

Answer 2

why do you multiply by 25 in the first answer (to find S25)
in the other two, you multiply by 9 to find S10

Answer 3

I thought that was the right way to solve it

Answer 4

I think they use S to represent SUM of the series. that uses a different formula.

The formula you are using finds the "nth term"
\[ a_n= a_1 + (n-1) d \]
in the first problem, you should use (25-1) i.e. 24
to find the 25th term. Can you fix that.

once you do, we go to the next step.

Answer 5

ok so we do this 1/2 + 25*(1/2) =

Answer 6

24* not 25

Answer 7

yes, what do you get ?

Answer 8

12.5

Answer 9

ok, next we use this formula to find the sum of the first n terms:
\[ S_n= \frac{n}{2} ( a_1 + a_n) \]
we need numbers to use this formula
for \(S_{25}\)
any idea what is n? what is a1 and what is a25?
(hint: a1 is ½ and a25 is what you just found)

Answer 10

Sn=n/2(1/2+12.5) correct?

Answer 11

yes, but you need a number for n. what is it ?

Answer 12

13?

Answer 13

you "match up"
\[ S_n \text{ with } S_{25} \]
to find n

Answer 14

in other words, n is the number of terms we are adding up
In this question, when they ask "what is \(S_{25} \) they are asking what is the sum of the first 25 terms. n is 25

Answer 15

ohhh ok

Answer 16

so you use the formula
\[ S_{25}=\frac{25}{2}(1/2+12.5) \]

Answer 17

ok so the formula is S25 = 25/2 (1/2+12.5) now we solve it right?

Answer 18

the word is "evaluate" (means "figure out using arithmetic")

Answer 19

im trying to solve this, but i need to know the common difference would it be 1/2?

Answer 20

Are you asking how to simplify
\[ S_{25}=\frac{25}{2}(0.5+12.5)\]
?

Answer 21

s25= 25/2 * 13 = 162.5

Answer 22

yes. that is the answer to the first question.

to review:

you need to find \(S_{25} \)
to do that , you use the formula:
\[ S_n= \frac{n}{2} (a_1+a_n) \]
with n= 25.
the first term \(a_1=\frac{1}{2} \)
but we still need to find the last term, \(a_{25} \)

so you use another formula to find \(a_{25} \):
\[ a_n = a_1+(n-1) d \]
to use this formula, we need the first term (which we have,it's ½)
we also need n (which we have, it's 25)
and we need d, the difference between each term. Looking at the numbers , we see d is ½
using those numbers, we figure out \(a_{25} \)
\[ a_{25}= \frac{1}{2} + (25-1)\cdot \frac{1}{2} \\
a_{25}= \frac{25}{2} = 12.5\]

now we go back, and figure out \(S_{25} \)

Answer 23

it's a bit complicated, but it is step by step.

can you do the 2nd problem ?

Answer 24

this is really complicated, but i'll continue practicing it till I get an idea of how to do it. Thank you for all your help!

Answer 25

For the second problem, you already figured out \(a_{10}\)\
so you know all the numbers that go into
\[S_n= \frac{n}{2}(a_1+a_n) \]
n is 10
\(a_1\) is 2
\(a_{10}\) is 29