Question

An arithmetic series contains 20 numbers. The first number is 102. The last number is 159. Which expression represents the sum of the series?

Answer 1

Answer: The expression is,

`(20)/(2)(102+159)`

Explanation:

Since, the sum of an A.P. is,

`S_n=(n)/(2)(a+a_n)`

Where, n is the number of terms,

a is the first term of the A.P.,

`a_n` is the last term of the A.P.,

Here, we have given,

a = 102,
`a_n` = 159, and n = 20,

Thus, the sum of the given A.P. is,

`S_20=(20)/(2)(102+159)`

Which is the required expression.