Question

What is the sum of a 14–term arithmetic sequence where the last term is 30 and the common difference is –5?

Answer 1

do you know the formula? lol

Answer 2

no i cant tell the difference between the 2 formulas

Answer 3

\[\LARGE S_n=\frac n2[2a_1+(n-1)d]\]
you're dealing with this one....
and this one
\[\LARGE a_n=a_1+(n-1)d\]

Answer 4

yeah idk how to tell which one applies to which equation.

Answer 5

from the second equation you have to find a_1 ... then to substitute into the first one , to find their sum.

Answer 6

where does the -5 go ?

Answer 7

d=-5

Answer 8

is An = 30 ? or 14

Answer 9

you have to find a_1 ...

Answer 10

is it - 145?

Answer 11

\[\LARGE a_{14}=a_1+(14-1)(-5)\]
\[\LARGE 30=a_1+13(-5)\]
\[\LARGE 30=a_1-65\]
\[\LARGE a_1=30+65\]
\[\LARGE a_1=95\]

Answer 12

now
\[\LARGE S_{14}=\frac{14}{2}[2\cdot 95+(14-1)\cdot (-5)]\]
can you do it? :)

Answer 13

see i dont get why it was 14 first then changed to 30
and no im not good with fractions

Answer 14

it changed to 30
because statement says:
What is the sum of a 14–term ...where the last term is 30
so it means a_14=30
that's why a_14 changed to 30

Answer 15

oh okayy, see i didnt know which one went where i didnt know that 14= 30

Answer 16

and don't worry about fractions...
\[\LARGE S_{14}=\frac{14}{2}[2\cdot 95+(14-1)\cdot (-5)]\]
\[\LARGE S_{14}=7\cdot [2\cdot 95+(14-1)\cdot (-5)]\]
now you don't have fractions ;) .. can you give it a try?

Answer 17

875

Answer 18

I don't know... give me a second to calculate it lol

Answer 19

okay

Answer 20

yes... 875 is correct . Well done :)

Answer 21

thank you