In an arithmetic sequence a14= -75 and a26 = -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 a14= -75 and a26 = -123, the recursive formula which defines the sequence is -19 - 4n.
Let's understand how we arrived at the solution.
For solving this question, we use the formula for finding nth term of AP: an = a + (n - 1)d, d = common difference, a = first term.
⇒ Hence, a14 = a + 13d = -75
⇒ a26 = 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 an = -19 - 4n.