How many terms are in this series?

[aisha]

I have a question is sigma notation

92
E (-7)^i+7
i=7

Is the number of terms in this series 99? Or

86, 89, or 96 I am so confused PLZ HELP IMMEDIATELY

I think it is 99 because 92+7=99 but I am not sure

 

[dextercioby]

Please write it more clearly.Is that "i" $\sqrt{-1}$...?

Use LaTex.

Daniel.

 

[aisha]

no its

(-7) to the exponent (i+7)

hurry help

 

[dextercioby]

So that "i" wanders through "n"...?

Daniel.

P.S.If so,then is 99 a natural power of 7...?

 

[shmoe]

Is this your sum?

$$\sum_{i=7}^{92}(-7)^{i-7}$$

You have a term for each number 7, 8, 9, ..., 91, 92. How many numbers on this list?

 

[dextercioby]

OMG,i didn't understand the question...No wonder the ballooney...

So it was that simple...

Daniel.

 

[Giuseppe]

I believe there are 86 in the terms. you take 92-7+1=86

 

[HallsofIvy]

Looks like a simple geometric sum to me.
$$\sum_{i=7}^{92}(-7)^{i-7}$$

Let n= i- 7 so that when i= 7, n=0 and when i= 92, n= 92-7= 85 (as Gieuseppe said).

The sum is the same as $$\sum_{n=0}^{85}(-7)^{n}$$.

Can you do that? (There is a simple formula for geometric sums.)

 

[aisha]

$$\sum_{i=7}^{92}(-7)^{i+7}$$

the exponent is i plus 7 not minus. Also the answer is 86 not 85 but I don't know how to get the answer I tried so many times.

 

[shmoe]

Can you answer the question how many numbers are on the list 7, 8, 9, ..., 92?

How about we subtract 6 from each number. The list:

7, 8, 9, ..., 92

has the same number of items as:

1, 2, 3, ..., 86



In general if you have a sum whose index ranges from a to b, you have b-a+1 terms.