# In an arithmetic sequence a_{14}= -75 and a_{26} = -123. Which recursive formula defines the sequence?

Arithmetic Progressions are a sequence of numbers having a common difference between two consecutive terms. They are very useful in fields of engineering, science and even in advanced mathematics. They have many interesting properties. Let's have a look at some of them in this question.

## Answer: In the arithmetic sequence a_{14}= -75 and a_{26} = -123, the recursive formula which defines the sequence is -19 - 4n.

Let's understand how we arrived at the solution.

**Explanation:**

For solving this question, we use the formula for finding nth term of AP: a_{n} = a + (n - 1)d, d = common difference, a = first term.

⇒ Hence, a_{14} = a + 13d = -75

⇒ a_{26} = a + 25d = -123

Solving the two above equations, we get: d = -4, a = -23.

Again, by using the nth term formula, we get the recursive formula to be a_{n} = -19 - 4n.