Dante is making a necklace with 18 rows of tiny beads in which the number of beads per row is given by the series 3+10+17+24+....
If you were to write this series in summation notation, give... 1. The lower limit of the sum
2. The upper limit of the sum
and 3. The explicit formula of the sum.

Question

Dante is making a necklace with 18 rows of tiny beads in which the number of beads per row is given by the series 3+10+17+24+....
If you were to write this series in summation notation, give... 1. The lower limit of the sum
2. The upper limit of the sum 
and 3. The explicit formula of the sum.

fortytherapper · Answer

The lower limit is in the form n = ?, where the ? is the beginning number. Do you see the beginning number? It's given actually

The upper limit is just a number, but it's the ending number. They gave this one too, if you see it?

anonymous · Answer

Oh okay, so the lower limit is 3 and the upper limit is 24??

anonymous · Answer

Is that correct?

fortytherapper · Answer

I didn't even know OpenStudy had this!

$$\sum_{n = ?}^{ending}Formula$$

But the answer lie within the row of beads. How many beads do we start with and how many do we end with?

anonymous · Answer

So 3 to infinity? I'm sorry, this question just confuses me.

fortytherapper · Answer

No worries

Say you wanted to make 18 rows of beads like Dante. How many rows (besides 0) would you start with and how many rows would you end with?

welshfella · Answer

this is an arithmetic sequence with common difference 7.
7 is added to get the next term

anonymous · Answer

oh lol start with 1 end with 18

anonymous · Answer

Yeah welsh, I see that...

fortytherapper · Answer

Right, so let's add those in

$$\sum_{n=1}^{18}Formula$$

welshfella · Answer

nthe term = a1 + (n -1)d
where a1 = first term and d = common difference
so the last (18th term) is
3 + (18-1)7

fortytherapper · Answer

Since 

Row 1 = 3
Row 2 = 10
Row 3 = 17

etc., 
now we wanna make a formula for it

welshfella · Answer

sum of n terms  = (n/2)[a1 + L]
where a1 = first term , L = last term)

n = 18 , a1 = 3 and L  is  3 + 17*7

anonymous · Answer

The pattern ends in 122

welshfella · Answer

yes

anonymous · Answer

So would that be the upper limit?

welshfella · Answer

yes

anonymous · Answer

So wait, how do I find the formula?

welshfella · Answer

Oh they want summation  notation . ......

anonymous · Answer

yes

welshfella · Answer

excuse me!!

anonymous · Answer

???

welshfella · Answer

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welshfella · Answer

the limits are 1 and 18

anonymous · Answer

Just f(n)? So  would it be 1(7)??

welshfella · Answer

and the expicit fformula for each term is a1 + (n - 1)d

anonymous · Answer

So 3+(18-1)7

welshfella · Answer

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