Find the sum of the arithmetic sequence. 17, 19, 21, 23, ..., 35 (1 point)
2 answers:
Answer:
260
Step-by-step explanation:
Given the first and last terms in the sequence , calculate the sum using
=
(a + l)
where a is the first term and l the last term
Here a = 17 and l = 35
To calculate the number of terms use the n th term formula
= a + (n - 1)d
where d is the common difference
a = 17 and d = 19 - 17 = 2 and = 35, thus
17 + 2(n - 1) = 35 ( subtract 17 from both sides )
2(n - 1) = 18 ( divide both sides by 2 )
n - 1 = 9 ( add 1 to both sides )
n = 10
Hence
= 5(17 + 35) = 5 × 52 = 260
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If the smaller truck makes 18 more trips than the larger
so,
number of trips for larger truck =x
number of trips for smaller truck =x+18
The capacities of two trucks are 3 tons and 4 tons respectively
so, capacity of smaller truck per trip =3 tons / trip
total ton carried by smaller truck = (number of trips for smaller truck)*(capacity of smaller truck per trip)
now, we can plug values
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Answer:
n = 8
Step-by-step explanation:
"By inspection" is an appropriate method.
We are asked to compare the expressions
n·n
8·n
and find the value(s) of n that makes them equal. <em>By inspection</em>, we see that n=8 will make these expressions equal. We also know that both expressions will be zero when n=0.
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More formally, we could write ...
n^2 = 8n . . . . the two formulas give the same value
n^2 -8n = 0 . . . . rearrange to standard form
n(n -8) = 0 . . . . . factor
Using the zero product rule, we know the solutions will be the values of n that make the factors zero. Those values are ...
n = 0 . . . . . makes the factor n = 0
n = 8 . . . . . makes the factor (n-8) = 0
Generally, we're not interested in "trivial" solutions (n=0), so the only value of n that is of interest is n = 8.
__
A lot of times, I find a graphing calculator to be a quick and easy way to find function argument values that make expressions equal.
