Question

What is the sum of a 23–term arithmetic sequence where the first term is 9 and the last term is 185?

1,472

1,725

2,231

2,478

Answer 1

Good question. Let's think for a minute. If we have an arithmetic sequence, we add the same thing over and over. So\[185=9+22k\]if k is that number we add over and over.

Answer 2

Looks like we add eight repeatedly.

Answer 3

soo what would be the answer?

Answer 4

Looks like you are only interested in the answer, than how to actually do the question.

Answer 5

I need the answer so I know i did it right

Answer 6

So the total is\[9+\sum_{1}^{22}9k=9(1+\sum_{1}^{22}k)=9(1+22*23/2)=9(254)=2286\]

Answer 7

Kay, sry for being offensive, just that this site has too many pple just looking for answers only.

Answer 8

its ok lol

Answer 9

Doesn't look like my answer meets the specifications of the multiple choice problem. Anybody see where I messed up?

Answer 10

I found the mistake. Just a second.

Answer 11

Sum of an arithmetic progression= n/2 ( first term + Nth term)
=23/2 (9+185)= 2231

Answer 12

the mistake lies in the 22 * (23/2). that makes no sense.

Answer 13

\[9+\sum_{1}^{22}(9+8k)=9+(22)9+8(22*23/2)=\]

Answer 14

22*23/2 is the sum of the first 22 numbers. That's a formula.

Answer 15

equals 23(9) + 253(8)=207+2024=2231

Answer 16

Darn, it's been a long time since I did one of these.....

Answer 17

My original mistake was to leave out the nine in the terms that were being summed. In addition, I calculated adding nine each time out of not paying attention to what I was doing.
Hope I was helpful.

Answer 18

tiaph, your solution is much more elegant than mine. I hadn't done one like this in a long time and tried brute force. Your solution is elegant.