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OpenStudy (lindseyhope123):
OpenStudy (lindseyhope123):
@jim_thompson5910 :) ha another, you seem to be really helping me today!
jimthompson5910 (jim_thompson5910):
what do you have so far?
OpenStudy (lindseyhope123):
i though n was 1, d was 3, and an was 60 and the final answer was 119 but i was wrong
jimthompson5910 (jim_thompson5910):
the sequence of pennies goes like this: 1, 3, 5, 7, 9, ...
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jimthompson5910 (jim_thompson5910):
what pattern is happening here?
OpenStudy (lindseyhope123):
plus 2
jimthompson5910 (jim_thompson5910):
yes
jimthompson5910 (jim_thompson5910):
so d = 2
jimthompson5910 (jim_thompson5910):
we'll use n = 60 because there are 60 terms here (from day 1 to day 60)
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OpenStudy (lindseyhope123):
okay
jimthompson5910 (jim_thompson5910):
Now we plug a1 = 1, d = 2 and n = 60 into the formula below to get...
\[\Large a_n = a_1 + d(n-1)\]
\[\Large a_n = 1 + 2(n-1)\]
\[\Large a_n = 1 + 2(60-1)\]
\[\Large a_n = ???\]
OpenStudy (lindseyhope123):
177?
jimthompson5910 (jim_thompson5910):
no
jimthompson5910 (jim_thompson5910):
you need to follow PEMDAS
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jimthompson5910 (jim_thompson5910):
you do NOT do 3*59 = 177
OpenStudy (lindseyhope123):
oops 119
jimthompson5910 (jim_thompson5910):
yes 119
jimthompson5910 (jim_thompson5910):
so
day 1 = 1 penny
day 2 = 3 pennies
day 3 = 5 pennies
day 4 = 7 pennies
...
...
...
...
day 60 = 119 pennies
OpenStudy (lindseyhope123):
so an and the final is both 119
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jimthompson5910 (jim_thompson5910):
now we use this formula
\[\Large S = \frac{n*(a_1+a_n)}{2}\]
plug in the values to get
\[\Large S = \frac{60*(1+119)}{2}\]
\[\Large S = ???\]
OpenStudy (lindseyhope123):
3600
jimthompson5910 (jim_thompson5910):
so....
n = 60
d = 2
a_n = 119 (when n = 60)
S = 3600
see attached
OpenStudy (lindseyhope123):
thank you
jimthompson5910 (jim_thompson5910):
be careful to type `3600` and not `3,600` otherwise the computer will think you're typing in 2 different values
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