Question

1. Write the formula for Arithmetic Series

​

Answer 1

Step-by-step explanation:

a n = n th term that has to be found

a 1 = 1 st term in the sequence

n = Number of terms

d = Common difference

S n = Sum of n terms

Arithmetic Series

A series such as 3 + 7 + 11 + 15 + ··· + 99 or 10 + 20 + 30 + ··· + 1000 which has a constant difference between terms. The first term is a1, the common difference is d, and the number of terms is n. The sum of an arithmetic series is found by multiplying the number of terms times the average of the first and last terms.

Formula:    or    

Example:

3 + 7 + 11 + 15 + ··· + 99 has a1 = 3 and d = 4. To find n, use the explicit formula for an arithmetic sequence.

We solve 3 + (n – 1)·4 = 99 to get n = 25.

or sum = 25/2 {2*3+(25-1)=1275

( I hope this was helpful ) >;D