SOLUTION: ( This might seem long but I tried to show what I did, and where I'm lost at.) Dante is making a necklace with 18 rows of tiny beads in which the number of beads per row is give

Question 1105091: ( This might seem long but I tried to show what I did, and where I'm lost at.)
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+...
a). If you were to write this series in summation notation, give...
i. the lower limit of the sum
ii. the upper limit of the sum
iii. the explicit formula of the sum
b). Find the total number of beads in the necklace. Explain your method for finding the total number of beads.
Me:
I tried to get this one ( Σ to answer for this question.) but I'm lost really, I do know that...
a.i.
18
Σ
n+7
and that's kinda it. I'm not really good when it comes to these types of math, but I want to get better at it. Could you please explain it to me? Thanks in advance! ^>^
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Look at the initial value 3.
To that, when n=0, 3+n=3 for the first value.
Every value after that goes up 7
So (3+7(0))+(3+7(1))+(3+7(2)) is the pattern.
So it is the sum of n=0 to 17 (that is 18 unique rows) of 3+7n.
Need to know a18, the 18th and final sum. That is 3+7(17)=122, the first row +the increase each row* the number of rows minus 1
Sum=(n/2)(a1+an)=(18/2)(3+122)=9*(125)=1125
3,10,17,24,31,38,45,52,59,66,73,80,87,94,101,108,115,122=1125

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