Question

What is the value of 143 + 163 + 183 + ... +303?​

Answer 1

Arithmetic series

Solution:

The given series is

143 + 163 + 183 + ... + 303

• First term is 143
• Second term is 163
• Third term is 183

Second term - First term = 163 - 143 = 20

Third term - Second term = 183 - 163 = 20

So the given series is an arithmetic series.

Let n th term is 303

Then, 143 + (n - 1) * 20 = 303

or, 143 + 20n - 20 = 303

or, 20n = 180

or, n = 9

So, given series has 9 terms.

Sum of the series is

= 9/2 * [143 + 303]

= 9/2 * 446

= 9 * 223

= 2007

Answer:

143 + 163 + 183 + ... + 303 = 2007