Find the first five terms of the sequence.an = 7 + 2na1 = a2 = a3 = a4 = a5 = Determine whether the sequence is arithmetic. If it is arithmetic, find the common difference d. (If the sequence is not arithmetic, enter DNE.)d = Express the nth term of the sequence in the standard form an = a + (n − 1)d. (If the sequence is not arithmetic, enter DNE.)
Question
Find the first five terms of the sequence.an = 7 + 2na1 = a2 = a3 = a4 = a5 = Determine whether the sequence is arithmetic. If it is arithmetic, find the common difference d. (If the sequence is not arithmetic, enter DNE.)d = Express the nth term of the sequence in the standard form an = a + (n − 1)d. (If the sequence is not arithmetic, enter DNE.)
Solution
The given sequence is an = 7 + 2n.
To find the first five terms of the sequence, we substitute the values of n from 1 to 5 into the formula.
a1 = 7 + 2(1) = 9 a2 = 7 + 2(2) = 11 a3 = 7 + 2(3) = 13 a4 = 7 + 2(4) = 15 a5 = 7 + 2(5) = 17
So, the first five terms of the sequence are 9, 11, 13, 15, 17.
To determine whether the sequence is arithmetic, we check if the difference between consecutive terms is constant.
a2 - a1 = 11 - 9 = 2 a3 - a2 = 13 - 11 = 2 a4 - a3 = 15 - 13 = 2 a5 - a4 = 17 - 15 = 2
Since the difference is constant, the sequence is arithmetic. The common difference d is 2.
The nth term of an arithmetic sequence can be expressed in the standard form an = a + (n − 1)d.
For this sequence, a = a1 = 9 and d = 2. So, the nth term is an = 9 + (n - 1)2.
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