(a) To find the first five terms of the sequence, we substitute the values n = 1, 2, 3, 4, and 5 into the formula an = 72 - (n - 1).

a1 = 72 - (1 - 1) = 72
a2 = 72 - (2 - 1) = 71
a3 = 72 - (3 - 1) = 70
a4 = 72 - (4 - 1) = 69
a5 = 72 - (5 - 1) = 68

(b) The common difference d in an arithmetic sequence is the difference between any two successive terms. In this case, it is a2 - a1 = 71 - 72 = -1.

(c) To graph the terms, you would plot the points (1, 72), (2, 71), (3, 70), (4, 69), and (5, 68) on a coordinate plane. The x-axis would represent the term number (n) and the y-axis would represent the term value (an). The points would form a straight line sloping downwards, reflecting the constant difference of -1 between each term.

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(a) To find the first five terms of the sequence, we substitute the values n = 1, 2, 3, 4, and 5 into the formula an = 72 - (n - 1).

a1 = 72 - (1 - 1) = 72
a2 = 72 - (2 - 1) = 71
a3 = 72 - (3 - 1) = 70
a4 = 72 - (4 - 1) = 69
a5 = 72 - (5 - 1) = 68

(b) The common difference d in an arithmetic sequence is the difference between any two successive terms. In this case, it is a2 - a1 = 71 - 72 = -1.

(c) To graph the terms, you would plot the points (1, 72), (2, 71), (3, 70), (4, 69), and (5, 68) on a coordinate plane. The x-axis would represent the term number (n) and the y-axis would represent the term value (an). The points would form a straight line sloping downwards, reflecting the constant difference of -1 between each term.

Knowee AI · Accepted Answer

(a) To find the first five terms of the sequence, we substitute the values n = 1, 2, 3, 4, and 5 into the formula an = 72 - (n - 1).

a1 = 72 - (1 - 1) = 72
a2 = 72 - (2 - 1) = 71
a3 = 72 - (3 - 1) = 70
a4 = 72 - (4 - 1) = 69
a5 = 72 - (5 - 1) = 68

(b) The common difference d in an arithmetic sequence is the difference between any two successive terms. In this case, it is a2 - a1 = 71 - 72 = -1.

(c) To graph the terms, you would plot the points (1, 72), (2, 71), (3, 70), (4, 69), and (5, 68) on a coordinate plane. The x-axis would represent the term number (n) and the y-axis would represent the term value (an). The points would form a straight line sloping downwards, reflecting the constant difference of -1 between each term.

The nth term of an arithmetic sequence is given.an = 72 − (n − 1)(a) Find the first five terms of the sequence.a1= a2= a3= a4= a5= (b) What is the common difference d?d = (c) Graph the terms you found in (a).

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