Question

sum of 1st 100 odd numbers =
pls... help me frnds
pls... say correct answers ​

Answer 1

Answer:

sum of first 100 odd numbers = 10000

Step-by-step explanation:

sum of 1st 100 odd numbers = 1 + 3 + 5 + ... 100terms

1,3,5,.. is  an Arithmetic progression, with

a= 1

d = 3-1 = 2

we know, Sₙ = (n/2)[2a+(n-1)d]

           => S₁₀₀ = (100/2) [ 2(1) + (100-1)2 ]

           => S₁₀₀ = 50 [ 2 + (99)2 ]

           => S₁₀₀ = 50 [ 2 + 198 ]

           => S₁₀₀ = 50 [ 200 ]

           => S₁₀₀ = 10000

another method,

sum of first n odd numbers = n²

so, sum of first 100 odd numbers = 100²

                                                       = 10000

Answer 2

Answer:

n = 100

Let a1 = 1, a2 = 3

a2 - a1 = d

3 - 1 = 2

So, d = 2

General term, aN = a + (n - 1)d

aN = 1 + (100-1)2

= 1 + 99 × 2

= 1 + 198 = 199

Sn = n/2 (a1 + a2)

= 100/2 (1 + 199)

= 50 × 200

= 10000

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