Question

find the sum of all odd number from 1 to 150​

Answer 1

Step-by-step explanation:

This is your answer

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Answer 2

Given:-

• An A.P 1, 3, 5, . . . . . , 149

To Find:-

• Sum of the A.P

Formula used:-

• ${\boxed{a_n= a+(n-1)d}}$

• ${\boxed{S_n=\dfrac{n}{2}(a+l)}}$

Solution:-

Here,

• a = 1

• d = 3 - 1 = 2

• $a_n\:or\:l\:=149$

Now,

$\implies\:a_n= a+(n-1)d$

$\implies\:149= 1+(n-1)2$

$\implies\:149= 1+2n-2$

$\implies\:2n=149+1$

$\implies\:n=\dfrac{150}{2}$

$\implies\:n=75$

Now using,

$\implies\:S_n=\dfrac{n}{2}(a+l)$

$\implies\:S_n=\dfrac{75}{2}(1+149)$

$\implies\:S_n=\dfrac{75}{2}\times150$

$\implies\:S_n=75\times75$

$\implies\:S_n=5625$

Hence, The sum of all odd numbers from 1 to 150 is 5625.

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More Formulas:-

• $S_n=\dfrac{n}{2}[2a+(n-1)d]$

• $S_n=\dfrac{n}{2}[a+a+(n-1)d]$

• $S_n=\dfrac{n}{2}(a+a_n)$

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