Write the sum using summation notation, assuming the suggested pattern continues.

Question

Write the sum using summation notation, assuming the suggested pattern continues.

-8 - 3 + 2 + 7 + ... + 67

summation of the quantity negative eight plus five n from n equals zero to fifteen
summation of negative forty times n from n equals zero to infinity
summation of negative forty times n from n equals zero to fifteen
summation of the quantity negative eight plus five n from n equals zero to infinity

 

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -24 and 1536, respectively.

an = 6 • (-4)n + 1
an = 6 • 4n
an = 6 • 4n - 1
an = 6 • (-4)n - 1

 

Find an equation for the nth term of the arithmetic sequence.a16 = 21, a17 = -1

an = 351 + 22(n + 1)
an = 351 - 22(n + 1)
an = 351 + 22(n - 1)
an = 351 - 22(n - 1)

Answer 1

-8,-3,2,7 ...

is an arithmetic sequence with common difference = d

a1 = -8

a2 = a1+d

a3 =a1 +2d

an =a1 +(n-1)d = -8 +(n-1)3 = -8 +3n-3 = 3n-11

sum of an arithmetic series = Sn= n(a1+an)/2

multiply the number of terms by the average of the 1st and last terms

for 1st three terms S3 = 3(-8+2)/2 = -9

capital Greek Sigma is used in place of the English capital S, with 1 at the bottom of the Sigma and n or 3 at the top of the Sigma. Capital Greek Sigma is sort of like an English capital M on its side, with bottom of the M facing right.