Question

What is the sum of a 22-term arithmetic sequence where the first term is 57 and the last term is -27

Answer 1

you need to know the numbers between

Answer 2

no just the sum of the numbers

Answer 3

ight then ig add all the numbers

Answer 4

so wat are the numbers in between..

Answer 5

well. I think since there are 22 terms and the first one is 57 and the last one is -27
it means that:
\[\LARGE a_1=57 \quad \quad ,\quad \quad a_{22}=-27\]
\[\LARGE a_{22}=a_1+(22-1)d\]
\[\LARGE -27=57+21d\]
... whoaa @eliassaab O_O :)

Answer 6

so wat would be my final answer my choices are A) 240
B) 270
C) 300
D) 330

Answer 7

@Kreshnik, Solve for d, d=-4

Answer 8

...so it means that d=-4
\[\LARGE Sn=\frac n2 [ 2\cdot a_1+(n-1)d]\]
\[\LARGE S_{22}=\frac{22}{2} [ 2\cdot 57+(22-1)(-4)]\]
\[\LARGE S_{22}=11 [ 114-84]\]
\[\LARGE S_{22}=11 [30 ]\]
\[\LARGE S_{22}=330\]

Answer 9

Here is the sequence
{57, 53, 49, 45, 41, 37, 33, 29, 25, 21, 17, 13, 9, 5, 1, -3, -7, \
-11, -15, -19, -23, -27}
And the sum is
330

Answer 10

@eliassaab well done. Great work ! ;)

Answer 11

thanks guys ;)