Write an expression for the nth term of the sequence, 15, 12, 9, 6, …

Solution:

An arithmetic progression is a sequence where the difference between every two consecutive terms is the same.

For a given arithmetic sequence, the nth term of AP is calculated using the following expression:

a_n = a + (n - 1) d

Where,

• 'a' is the first term of the AP
• 'd' is the common difference
• 'n' is the number of terms
• 'a_n' is the n^th term of the AP.

Let's find the nth term of the sequence, 15, 12, 9, 6, …

Here, a = 15, d = -3, n = n

Thus, substituting these values in the formula

a_n = a + (n - 1) d

⇒ a_n = 15 + (n - 1) (-3)

⇒ a_n = 15 + 3 - 3n

⇒ a_n = 18 - 3n

Thus, the expression for the n^th term of the sequence, 15, 12, 9, 6, … is a_n = 18 - 3n.

We can use Cuemath's Online Arithmetic sequence calculator to find the arithmetic sequence using the first term and the common difference between the terms.

Hence, the expression for the n^th term of the sequence, 15, 12, 9, 6, … is a_n = 18 - 3n.

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Write an expression for the nth term of the sequence, 15, 12, 9, 6, …

Summary:

The expression for the n^th term of the sequence, 15, 12, 9, 6, … is a_n = 18 - 3n