Question

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

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

Answer 1

you are not here, so I can write whatever I want, no need to worry that I cannot answer your questions, hehehe

Answer 2

first of all, do you see the difference between the numbers is 5. what does it mean?
it means the second number will be 5 units bigger than the first one, the third one will be 5 units bigger than the second one, so on and so on....

Answer 3

however, when counting the sum, you must find out the general form in which you can find out any number you like in sequence without depending on the previous term,
do you know what I mean?

Answer 4

hhmmm, for example: you can count the 2nd number by adding 5 into the 1st one and you have a_2 = a_1 +5
and then a_3= a_2 +5
and then a_4 = a_3 +5 so on and so on....

Answer 5

the inconvenience of that method is you must find out the term before the term you want to know. What if they ask you find out the 100th term? you must count a-1, a_2, a_3,........ to a_99 to get a_99 +5 = a_100, right?

Answer 6

OMG, you waste your time. Fortunately, you have another way to figure out the "whatever"term you need by general form. How to get it? quite easy

Answer 7

start at a_1 = -8
a_2 = -8 +5
a_3 = a_2 +5 but as above, we have a_2 = a_1 +5 waha... just plug into a_3. So, a_3 = a_1 +5 +5 = a_1 + 2*5 . Pay attention here. I don't write 10 but 2*5, why? because I want you to see the link between the order of a_ to that number . It's a_3 then that number is 2 [ I note them as n=3 and 2 =n-1]
Now, continue a_4 = a_3 + 5 = a_2 +5 +5 = a_1 +5 +5 +5 = a_1 + 3*5. You see!! now, i have a_4 = a_1 + 3*5 [ as I noted above, now, my n =4 and that number is n-1 =3]

Answer 8

from this fact, now I can conclude that my general form of the sequence is
a_n = a_1 + (n-1) *5
in your case, you have a_1 = -8 so a_n = -8+(n-1)*5
by that form, you can count how many number you have in the sequence
the last term of your sequence is 67 . Ir means -8 +(n-1) *5 = 67, hence, n=???
calculate it , you have n = 16. that means you have 16 terms in the sum.

Answer 9

Now, combine all of information we have. What do we have? we have general form a_n, we have the number of terms is 16 so, just rewrite under the sum notation
\[\sum_{n=1}^{16}-8 +(n-1)*5\]
That's it.

Answer 10

There is someone told me that "try to teach something, not just give out the answer" . I just said sorry for being lack of that skill, ha!! Now I dip you into the pool of information.
Read it or not depend on you. me done