Question

find the sum without actually adding the following odd numbers: the first 99 odd natural numbers . the correct answer is 9801 . please let me know the answer fast.​

Answer 1

Answer:

we know that sum of n terms of ap is

n (2a +(n-1)d)

2

and for the odd no we have

n=99

a=1

d=2

Step-by-step explanation:

99÷2 (2+[98×2])

99÷2(2×99)

99(99×2)

2

now 2 in denominator and numerator is cancelled

and 99×99=9801

Answer 2

Answer:

The sum of the first 99 odd natural numbers is 9801

Step-by-step explanation:

This is an arithmetic progression, so we need to find its sum.

The formula for getting the sum of the first n terms of an arithmetic progression is given as follows:

S = n/2 {2a + (n - 1)d}

n = the number of terms

a = the first term

d = the common difference

The first odd number is 1 which in this case is the first term.

the common difference between odd numbers is 2

n = 99

Therefore, S = 99/2 × {2 × 1 + (99 - 1)2}

= 49.5 × 198 = 9801