Calculates AP Series. when the, nth, first and last terms are given.\[a_n= a+d\]
An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. The terms in an arithmetic progression can be described using a general formula, which helps in quickly identifying the value of any term in the sequence.
This formula is derived by adding the common difference to the first term and multiplying it by the term number minus one. By understanding the concept of arithmetic progression terms, students can easily solve problems related to finding missing terms, determining the sum of a certain number of terms, or even predicting future terms in the sequence.
First Identify and note down the given values:
The term number (n)
The first term (a1)
The last term (l)
Use the formula for the n-th term of an arithmetic progression when the first and the last terms are given, so the arithmetic progression for the nth terms, where the difference 'd' is unknown is computed using
a_n= a1 + d
Determine the unknown "d" using the formula below
difference, d = first - last term/n+1
Next, substitute the value of d from expression below into the original formula
a_n= a1 + d
Generate the next n-terms series using the difference between the last and the first number in the series
