Question

What is the sum of the first 30 odd numbers?

• A. 900
• B. 875
• C. 870
• D. 920

Answer 1

The correct option is A

900

Every term is of the form 2n + 1, i.e. the sequence is 1,3,5,…

First term, a = 1

Common difference, d = 2
Then the 30th odd term will be:

$\Rightarrow T_{30}=a+(n-1)d=1+(30-1)2=59$

$\Rightarrow Sumofnterms=\frac{n}{2}(a+l)$ , where $l=T_{30}$

$\Rightarrow Sumofnterms=\frac{30}{2}(1+59)$

$\Rightarrow Sumto30terms=15\times 60=900$