# Thread: arithmetic sequence, determine sum

1. ## arithmetic sequence, determine sum

In an arithmetic sequence, the fifth is 21 and the eighth is 3.
Determine

a) the first number of the sequence
b) the sum of the sixteen first numbers.

a) I got the answer to 45. So a1=45

But I can't solve b, because I get a completely different answer than what I should get. (the answer should be 0)

I thought:

n=16
a1=45
d=-6

an=a1+(n-1)*d

an=45+(16-1)*(-6)

an=45-90

an=-45

sum=(n/2)*(a1+an)

sum=(16/2)*(16+(-45))

sum=8*(-29)= -232

so I got the sum to -232, but it should be 0. How did I think wrong?

2. ## Re: arithmetic sequence, determine sum Originally Posted by selin In an arithmetic sequence, the fifth is 21 and the eighth is 3.
Determine

a) the first number of the sequence
b) the sum of the sixteen first numbers.

a) I got the answer to 45. So a1=45

But I can't solve b, because I get a completely different answer than what I should get. (the answer should be 0)

I thought:

n=16
a1=45
d=-6

an=a1+(n-1)*d

an=45+(16-1)*(-6)

an=45-90

an=-45

sum=(n/2)*(a1+an)

sum=(16/2)*(16+(-45))

a1 is not 16, should be (16/2)*[45 + (-45)]

sum=8*(-29)= -232

so I got the sum to -232, but it should be 0. How did I think wrong?
see correction above

3. ## Re: arithmetic sequence, determine sum Originally Posted by Cervesa see correction above
Thank you.