Given a sequence a 1 , a 2 , a 3 , … , a n , the arithmetic mean a ¯ is given by a ¯ = 1 n ∑ i = 1 n a i . Use the arithmetic mean for Exercises 103-104. Consider the sequence defined by a n = 18 , 32 , 44 , 20 , 36 , 28 , 32 , 38 . Evaluate ∑ i = 1 8 a i − a ¯ 2 .
Given a sequence a 1 , a 2 , a 3 , … , a n , the arithmetic mean a ¯ is given by a ¯ = 1 n ∑ i = 1 n a i . Use the arithmetic mean for Exercises 103-104. Consider the sequence defined by a n = 18 , 32 , 44 , 20 , 36 , 28 , 32 , 38 . Evaluate ∑ i = 1 8 a i − a ¯ 2 .
Solution Summary: The author calculates the sum of terms of the sequence with a total of n terms.
Given a sequence
a
1
,
a
2
,
a
3
,
…
,
a
n
, the arithmetic mean
a
¯
is given by
a
¯
=
1
n
∑
i
=
1
n
a
i
. Use the arithmetic mean for Exercises 103-104.
Consider the sequence defined by
a
n
=
18
,
32
,
44
,
20
,
36
,
28
,
32
,
38
. Evaluate
∑
i
=
1
8
a
i
−
a
¯
2
.
A 20 foot ladder rests on level ground; its head (top) is against a vertical wall. The bottom of the ladder begins by being 12 feet from the wall but begins moving away at the rate of 0.1 feet per second. At what rate is the top of the ladder slipping down the wall? You may use a calculator.
Explain the focus and reasons for establishment of 12.4.1(root test) and 12.4.2(ratio test)
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