Answer:
25 000 000
Step-by-step explanation:
The sum of the first [tex]n[/tex] odd numbers is [tex]n^{2}[/tex]
For example,
when [tex]n=1[/tex] ⇒ [tex]1 = 1^2[/tex]
when [tex]n = 2[/tex] ⇒ [tex]1 + 3 = 4 = 2^2[/tex]
when [tex]n = 3[/tex] ⇒ [tex]1 + 3 + 5 = 9 = 3^2[/tex]
So the sum of the first 5000 odd numbers is [tex]5000^{2} =25\ 000\ 000[/tex]
The sum of the first 5000 odd numbers is 25,000,000
Odd numbers are numbers that when divided by 2 will give a remainder. Therefore, the sequence will be
1, 3, 5, 7, 9, 11,.......
From the sequence, the first term is 1 and the common difference is 2. Therefore,
a = 1
d = 2
Using sum formula for arithmetic progression,
Sₙ = n / 2(2a + (n - 1)d)
n = 5000
S₅₀₀₀ = 5000 / 2 (2 × 1 + (5000 - 1)2)
S₅₀₀₀ = 2500 (2 + (9998 ))
S₅₀₀₀ = 2500(10,000)
S₅₀₀₀ = 25,000,000
The sum of the first 5000 odd numbers is 25,000,000
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