Question

can someone show me how to do this??...find the sum of the given arithmetic series
30+23+16+9+...+(-33)
a. -15
b. 315
c. -3
d. -30

Answer 1

Here

a = 30,

d = 23 - 30 = -7

Use:

\[\large a_n = a + (n-1)d\]

So:

\[30 + (n - 1)(-7) = -33 \implies -7n = -70\]

\[n = 10\]

Now use:

\[\large Sum = \frac{n}{2}(a + a_n)\]

Answer 2

notice first:
30+23+16+9+...+(-33)
-33 +...+ 9+16+23+30
-----------------------
3 +3 +...........+3 + 3

then find how many terms you series has
multiply 3 by this number and devide by 2

Answer 3

\(a_n\) is the last term here that is -33..

n = 10 here..

a = 30 here..

Answer 4

oo okay i see, my formula was wrong! i was divided a+an by 2 instead of the n!

Answer 5

thanks for the help:))

Answer 6

It is okay..