Question

find the sum of 1+3+5+7_____+27+29 a.125 b.225 c.175 d.250​

Answer 1

Answer:

The sum 1+3+5+...+27+29 is 225.

Step-by-step explanation:

We need to find the sum of odd numbers starting from 1 to 29.

Consider these numbers as an arithmetic progression with the first term$(a)$ 1 and common difference$(d)$ 2.

The $n^{th}$ term of this sequence is

$1+(n-1)2=2n+1-2=2n-1$

To find the value of $n$ when the term is 29.

$29=2n-1 \implies 29+1=2n\implies 2n=30\implies n=15$

So $15^{th}$ term of the progression is 29. Thus we need to calculate the sum of  the first 15 terms of the A.P. Using the formula for sum, we have

$Sum =\dfrac{n}{2}(2a+(n-1)d )=\dfrac{15}{2}(2\times 1+(15-1)2)\\\\= \dfrac{15}{2}(2+(14)2)=\dfrac{15}{2}(2+28)=\dfrac{15}{2}\times 30=15\times 15=225$

So the sum is 225, option(b).