Question 945097: Determine the number of terms n in each arithmetic series.
Problem 1: a1= 4, d = 7, Sn= 228
Problem 2: (−2) + (−12) + (−22) + (−32)..., Sn= −224
These problems stumped me...thanks in advance for your time and effort, I appreciate the help!
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Both problems require the formula to find the nth term of an arithmetic sequence:
Sn = A1 + (n-1)d
where
Sn is "sum of n terms"
A1 is the first term
n is the number of terms
d is the distance
.
Problem 1: a1= 4, d = 7, Sn= 228
Sn = A1 + (n-1)d
substitute the values given from the problem:
228 = 4 + (n-1)7
228 = 4 + 7n-7
228 = 7n-3
231 = 7n
33 = n
.
Problem 2: (−2) + (−12) + (−22) + (−32)..., Sn= −224
distance (d) is:
-12 - (-2) = -12 + 2 = -10
.
Sn = A1 + (n-1)d
substitute the values given from the problem:
-224 = -4 + (n-1)-10
-224 = -4 + -10n+10
-224 = -10n+6
-230 = -10n
23 = n
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