Question

Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15.
n an
1 5
2 −10
3 20

Answer 1

well it looks like the term is

\[5 \times (-2)^{n - 1}\]

so the sigma notation is

\[\sum_{n = a}^{b} 5 \times (-2)^{n - 1}\]

you just need the a and b values...

Answer 2

how do i do that @campbell_st

Answer 3

@Melodysim

Answer 4

Okay you dont have to use that @brynna

Answer 5

well it you look at

\[5\times (-2)^{n - 1}\]

when n = 1 the answer is

\[5 \times (-2)^{1 - 1} = 5\]

when n = 2 its

\[5 \times (-2)^{2 - 1} = -10\]

if you keep going you get the pattern

so the sigma notation is an abbreviation for the sum of the terms...

the question says start at 4 and finish the sum at 15

so its

\[\sum_{n = 4}^{15} 5 \times (-2)^{n - 1}\]

Answer 6

geometric sequence

Answer 7

so that will be the formula.

Answer 8

now a1 stands for first term