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Find the first five terms of the sequence.an = 15 + 3na1  =  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 = 15 + 3na1  =  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.)

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Solution

The sequence is defined by the formula an = 15 + 3n.

To find the first five terms of the sequence, we substitute the values n = 1, 2, 3, 4, and 5 into the formula:

a1 = 15 + 31 = 18 a2 = 15 + 32 = 21 a3 = 15 + 33 = 24 a4 = 15 + 34 = 27 a5 = 15 + 3*5 = 30

So, the first five terms of the sequence are 18, 21, 24, 27, and 30.

This sequence is arithmetic because the difference between consecutive terms is constant.

To find the common difference d, we subtract the first term from the second term:

d = a2 - a1 = 21 - 18 = 3

The nth term of the sequence in the standard form an = a + (n − 1)d is given by

This problem has been solved

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