Question

What is the nth term of the arithmetic sequence (7, 9, 11, 13, 15, 17...?)?

(a) n + 6
(b) 2n + 5
(c) 3n + 4
(d) 4n + 3

Answer 1

The nth term of the arithmetic sequence (7, 9, 11, 13, 15, 17...) is 2n + 5, determined by using the general formula for the nth term of an arithmetic sequence.

Step-by-step explanation:

To find the nth term of an arithmetic sequence, we need to use the formula for the nth term, which is an = a1 + (n - 1)d, where a1 is the first term and d is the common difference between the terms of the sequence. In this sequence (7, 9, 11, 13, 15, 17...), the first term a1 = 7 and the common difference d = 2. Thus, the formula for the nth term becomes an = 7 + (n - 1)×2, which simplifies to an = 7 + 2n - 2 or an = 2n + 5. Therefore, the correct answer is (b) 2n + 5.

Answer 2

The nth term of the arithmetic sequence (7, 9, 11, 13, 15, 17...) is found by using the formula for the nth term of an arithmetic sequence, which given the first term as 7 and the common difference as 2, simplifies to 2n + 5. Therefore, the correct option is (b) 2n + 5.

Step-by-step explanation:

The student has asked to identify the nth term of the arithmetic sequence (7, 9, 11, 13, 15, 17...). To find this, we can use the formula for the nth term of an arithmetic sequence:

Tn = a + (n - 1)d

Where Tn is the nth term, a is the first term, d is the common difference, and n is the position of the term in the sequence.

In this sequence, the first term is 7 and the common difference is 2 (since each term increases by 2). The formula becomes:

Tn = 7 + (n - 1)2

Simplifying further, we get:

Tn = 7 + 2n - 2

Tn = 2n + 5

Therefore, the correct option is (b) 2n + 5.