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.
Answers
Answered by
6
Answer:
9801
Step-by-step explanation:
1,3,5,7,.....,99th term
a=1
d=3-1=2
n=99
Sn=n/2[2a+(n-1)d]
Sn=99/2[2(1)+(99-1)2]
Sn=99/2[2+(98)2]
Sn=99/2[2+196]
Sn=99/2[198]
Sn=99×99
Sn=9801
Please mark it as brainliest
Answered by
2
Hi mate,
we solve it by 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
I hope it helps you.
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