Question

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

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

Answer 1

@IrishBoy123

Answer 2

this one is arithmetic, right?

so what is the common difference?

Answer 3

5

Answer 4

yes

so
\(a_1 = -8\)
\(a_2 = -8 + 1(5)\)
\(a_3 = -8 + 2(5)\)

we will want a general term for \(a_n\), the nth term in this sequence

Answer 5

can you have a go at that?

Answer 6

Would it be:\[\sum_{n=0}^{\infty}(-8+5n) \]

Answer 7

@IrishBoy123

Answer 8

if we are starting at n = 1, you need a small tweak

Answer 9

if term 1 is \(a_1\), with \(n = 1\)

Answer 10

sum_{n=0}^{15}(-8+5n) ?

Answer 11

\[\sum_{n=0}^{15}(-8+5n)\]

Answer 12

\(a_1=−8 = -8 +5(1-1)\)
\(a_2=−8+(5)(2-1)\)
\(a_3=−8+(5)(3-1)\)

Answer 13

\(a_n = ??\)

Answer 14

-8+5n

Answer 15

-8+5(n - ??)

Answer 16

That's not an answer choice though.

These are my answer choices:
A. \[\sum_{n=0}^{15}(-8+5n)\]

B. \[\sum_{n=0}^{\infty}(-40n)\]

C.\[\sum_{n-0}^{15}(-40n)\]

D. \[\sum_{n=0}^{\infty}(-8+5n)\]

Answer 17

OK, they're doing it that way, with the first term as \(a_0\) not \(a_1\)

in which case you go with your suggestion, \(-8+5n\)

and checking the value of \(n\) for the last term:

\(-8+5n = 67 \implies n = 15\)

Answer 18

Ok thanks! So it would be A?

Answer 19

\( \huge \checkmark \)