Question

find the sum of these 75 numbers 1+3+5+......+149

Answer 1

Answer:

the answer is 2275.....

Step-by-step explanation:

Answer 2

If you check into the numbers carefully, you will see that these numbers are forming an AP (Arithmetic Progression).

When we have to deal with an AP, the first thing we have to do is write the major values for the further solving.

a = 1

d = 2

$a_{75} = 149$

We need to find the sum of all the numbers present in this AP.

For doing this, we have two formulae.

Sⁿ = n/2[2a+(n-1)d]

Or

Sⁿ = n/2[a+aⁿ]

In this case, we are provided with aⁿ. Thus, we will ignore the first formula and use the latter.

So,

$s_{75} = \frac{75}{2} (1 + 149) \\ \\ s_{75} = \frac{75}{2} \times 150 \\ \\ s_{75} = 75 \times 75 \\ \\ s_{75} = 5625$

Hence, the sum of all the numbers present in the given series will be 5625.

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