Question

Find the first five terms of the sequence and determine if it is arithmetic. If it is arithmetic, find the common difference and express the n th term of the sequence in the standard form an=a+(n-1)d. an = 4+7 n

Answer 1

The given sequence is an arithmetic sequence with a common difference of 7. The first five terms are 11, 18, 25, 32, and 39.

Step-by-step explanation:

The given sequence is an example of an arithmetic sequence. To find the first five terms, we substitute the values of n from 1 to 5 into the given expression:

a1 = 4 + 7(1) = 11

a2 = 4 + 7(2) = 18

a3 = 4 + 7(3) = 25

a4 = 4 + 7(4) = 32

a5 = 4 + 7(5) = 39

The common difference in an arithmetic sequence is the difference between consecutive terms. In this case, the common difference is 7. The nth term of an arithmetic sequence can be expressed in the standard form as an = a + (n-1)d, where a is the first term and d is the common difference.