Question

(1 + 3 + 5 +............. + 17) + ( 2 + 4 + 6........ + 18) ​

Answer 1

The sum is 171.

Step-by-step explanation:

The expression is:

S = (1 + 3 + 5 +............. + 17) + ( 2 + 4 + 6........ + 18) ​

⇒ S = 1 + 2 + 3 + 4 + 5 + 6 + ... + 17 + 18

The series in an arithmetic progression.

The expression of S is the sum of first n = 18 terms with common difference, d = 1 and first term as a = 1.

Compute the value of S as follows:

$S=\frac{n}{2}[2a+(n-1)d]$

   $=\frac{18}{2}[(2\times 1)+(18-1)(1)]$

   $=9\times [2+17]\\=9\times 19\\=171$

Thus, the sum is 171.

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