arithmetic sequence, determine sum

May 2017
16
0
hold your rongue
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?
 
Dec 2014
165
125
USA
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
 
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