Question

What is the sum of the arithmetic sequence 135, 123, 111.. if there are 32 terms?

Answer 1

\[s _{n} = \frac{n}{2}[2a + (n-1)d]\]

in theis question 1st term a = 135, number of terms n = 135 and common difference d= -12

substitute them into the formula and evaluate

Answer 2

oops n = 32

Answer 3

I am confused on what to do.

Answer 4

\[a _{n} = a _{1} + (n - 1)d\]
\[a _{n} = 135 + (32 - 1)-12\]
\[a _{n} = 135 + (31)(-12)\]
\[a _{n} = 135 + (31)(-12)\]
\[a _{n} = 135 - 372\]
\[a _{n} = -237\]
\[S_{n} = n/2(a_{1} + a_{n})\]
\[S_{n} = 32/2(135 - 237)\]
\[S_{n} = 16(-102)\]
\[S_{n} = -1632\]

Answer 5

both methods shown use the idea of the sum of the 1st and last term multiplied by the number of terms over 2 will give the sum

do you know how to find a term in an arithmetic series...?

Answer 6

No.

Answer 7

so you know any formula for an arithmetic series...?

Answer 8

no. Can you please just give me the answer? Because I have to be done with this in 30 minutes to graduate.