Write the sum using summation notation, assuming the suggested pattern continues. -9 - 4 + 1 + 6 + ... + 66

Question

A. summation of negative forty five times n from n equals zero to fifteen
B. summation of the quantity negative nine plus five n from n equals zero to fifteen
C. summation of the quantity negative nine plus five n from n equals zero to infinity
D. summation of negative forty five times n from n equals zero to infinity

Answer 1

The formula for an arithmetic sequence is a_n = a₁ + d(n-1). You know it's arithmetic since this is repeated addition.

 

You know a₁= -9 and d= 5, so your sequence has the formula a_n= -9+5(n-1) = 5n-14

 

So now you can set that equal to 66 to find out which term number this is.

5n-14=66

5n = 80

n=16

 

So the 16th term is 66.

 

So you have the summation from 1 to 16 of the expression 5n-14. 

 

Unfortunately, this is not one of your choices....so they have a different form of this answer. All summations can be changed with respect to their indeces.

 

So if we switch the indeces to vary from 0 to 15, we must change the function by adding 5.

 

So you get the summation from 0 to 15 of the expression 5n-9.

 

Hope this helped.