The 38th term
This is an Arithmetic Progression with a first term (a) of 3, and a common difference (d) of 5. The formula for the nth term is a(n) = a + (n - 1)d. Then, 78 = 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2 Thus, 5n = 78 + 2 = 80 And so, n = 80/5 = 16 The 16th term of this AP is 78.
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4 10 16 22 28 34 40 ....... Each term is increased by 6 or nth term = 6n-2
If the first term, t(1) = a and the common difference is r then t(n) = a + (n-1)*r where n = 1, 2, 3, ...
The 38th term
Any number can be the nth term of a suitable AP.
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This is an Arithmetic Progression with a first term (a) of 3, and a common difference (d) of 5. The formula for the nth term is a(n) = a + (n - 1)d. Then, 78 = 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2 Thus, 5n = 78 + 2 = 80 And so, n = 80/5 = 16 The 16th term of this AP is 78.
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This cannot be shown because it is not true. The 29th term will be double the 19th.
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To receive help with the AP statistics investigative task answers for chapter 21 it is best to contact the instructor. This will insure that the correct methods for solving the problems is given. There are not any answers available online for this.