Question

Find the sum of the first 9 terms of the sequence.

2, -7, -16, -25, ...

Answer 1

do you see any pattern in your sequence ?

Answer 2

Well the difference between the three numbers to the right are all 9, but the difference between 2 and -7 is only 5 sooo I'm a little confused. @hartnn

Answer 3

How do I figure out what the other numbers are?

Answer 4

the difference between 2 and -7 :

\(\Large 2 - (-7) = 2+7 = 9 \\ \large \ddot \smile \)

Answer 5

Ohhhhhh! So it would be:

\[2, -7, -16, -25, -34, -43, -52, -61, -70 = -306\]

Answer 6

I feel like that's wrong though

Answer 7

Wouldn't I need to make some of the numbers positive? Would numbers -34 and -70 actually be positive? @hartnn

Answer 8

why you need to make them positive ??

since we have a common difference of -9 ,
this sequence is arithmetic sequence.
Have you taught how to find sum of terms in arithmetic sequence ?
any formula ?

Answer 9

Formula? No. I'm just supposed to add them all together once I know what the numbers are, right? So is my answer of -306 wrong?

Answer 10

There is an easier way to do it, using formula :
\(\large S_n = (n/2)[2a+ (n-1)d]\)

where,
n= number of terms
a = 1st term
d = common difference

(imagine if you're asked sum of 1000 terms...would you literally add 1000 terms ?)

Answer 11

for your problem, first term = a = 2
d= common difference = -9
and since we need sum of 9 terms , n = 9

Answer 12

And if you apply that formula, you get -306
indication you're anyways corrrect! :)

Answer 13

Cool! Thank you so much! @hartnn

Answer 14

welcome ^_^