Question

PLEASE HELP ME I WILL AWARD MEDAL!!!!!!!!!!!!!!!!!

Identify the 25th term of the arithmetic sequence 2, 1 and 3/5, 1 and 1/5?

–7 and 3/ 5

–8

–12 and 2/5

–13

Answer 1

@terenzreignz @whpalmer4

Answer 2

I'm not sure I know what the sequence is from that description.

Answer 3

@whpalmer4 I fixed the question.

Answer 4

@Hero

Answer 5

What is the common difference?

Answer 6

If it is not in the question then it is not their.

Answer 7

"there"

No, it isn't listed, you have to compute it! What is the difference between successive terms in this arithmetic sequence?

Answer 8

Oh I am sorry can you please explain to me.

Answer 9

What is the first term in the sequence?
What is the second term in the sequence?
What do you get if you subtract the second term from the first term?

What is the third term in the sequence?
What do you get if you subtract the third term from the second term?

See a pattern?

Answer 10

S=-2/5

Answer 11

Any idea how you're going to work out the value of the 25th term, knowing the value of the first term, and the common difference?

Answer 12

No not really.

Answer 13

If you know the first term is 2, how would you find the second term?

Answer 14

You just subtract 2/5 from each term.

Answer 15

So, you obtain the second term by subtracting the common difference from the first term. How do you obtain the third term?

Answer 16

Thank you I got the answer -7 3/5

Answer 17

Great! If you had to find the 8376th term, without the benefit of an answer list to choose from, could you?

Answer 18

Yes.

Answer 19

what would it be?

Answer 20

It will be -3350 and 2/5 correct?

Answer 21

oh, so close :-)

\[2 - \frac{(8376-1)*2}{5} = 2-\frac{8375*2}{5} = -3348\]

Answer 22

Sorry I meant -3348 and 2/5 Because I forgot to subtract from the 2. HA

Answer 23

that would be closer, but the answer is -3348.

If the first term is \(a_1\), and the common difference is \(d\), the formula for the \(n\)th term is \[a_n = a_1+d n + c\]We can find the value of \(c\) by setting \(n = 1\):
\[a_1 = a_1 + d(1) + c\]Subtract \(a_1\) from both sides
\[0 = d+c\]\[c = -d\]So our formula for \(a_n\) is
\[a_n = a_1 + d n -d\]or \[a_n = a_1 + d(n-1)\]

In our case, we had \(d = -2/5, n = 25, a_1 = 2\) so \[a_n = 2 - \frac{2}{5}(n-1) = 2+\frac{2}{5}-\frac{2}{5}n = \frac{12}{5}-\frac{2}{5}n\]

Answer 24

Thank you so much.