4950 is a sum of number series from 1 to 99 by applying the values of input parameters in the formula.

Sum of first odd number = 1. Sum of first two odd numbers = 1 + 3 = 4 (4 = 2 x 2). Sum of first three odd numbers = 1 + 3 + 5 = 9 (9 = 3 x 3). Sum of first four odd numbers = 1 + 3 + 5 + 7 = 16 (16 = 4 x 4).

S100=n2[2a+(n−1)d]substituting the values. we getS100=1002[2×1+(100−1)×1]S100=50[2+99]S100=50×101S100=5050∴ The sum of first 100 natural numbers is 5050.

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An example of AP is natural numbers, where the common difference is 1. Therefore, to find the sum of natural numbers, we need to know the formula to find it….Sum of N Terms of AP And Arithmetic Progression.

To find the sum of a finite geometric series, use the formula, Sn=a1(1−rn)1−r,r≠1 , where n is the number of terms, a1 is the first term and r is the common ratio .

The sum of the terms of a sequence is called a series . If a sequence is arithmetic or geometric there are formulas to find the sum of the first n terms, denoted Sn , without actually adding all of the terms.

The Sum to Infinity An infinite series has an infinite number of terms. The sum of the first n terms, Sn , is called a partial sum. If Sn tends to a limit as n tends to infinity, the limit is called the sum to infinity of the series. a = 1st Term. r = 2nd Term ÷ 1st Term.

The sum of all the odd integers from 1 to 50 is 625.

The number series 2, 4, 6, 8, 10, 12, . . . . , 100. Therefore, 2550 is the sum of first 50 even numbers.

Answer: The sum of first 20 odd natural numbers is 400.

Sum of first n even numbers = n * (n + 1).

The number series 2, 4, 6, 8, 10, 12, . . . . , 60. Therefore, 930 is the sum of first 30 even numbers.

To find the sum of first n odd numbers we can apply odd number theorem, it states that the sum of first n odd numbers is equal to the square of n. if we apply odd number theorem: sum of first 10 odd numbers = n * n = 10 * 10 = 100.

Note that the numbers may be paired off (1+99) , (3+97) , (5+95) , each pair adding to 100 . There are 25 such pairs. So the sum equals 2500 (25×100) .

The number series 1, 3, 5, 7, 9, . . . . , 73. Therefore, 1369 is the sum of first 37 odd numbers.

960

The number series 1, 3, 5, 7, 9, . . . . , 29. Therefore, 225 is the sum of first 15 odd numbers.

The number series 1, 3, 5, 7, 9, . . . . , 19. Therefore, 100 is the sum of first 10 odd numbers.

⇒Mean=Sn, where S represents the sum of the observations and n represents the number of observations. ∴ the mean of the first five odd natural numbers is 5. Hence, the correct option is (A).

Answer: The number series 2, 4, 6, 8, 10. Therefore, 30 is the sum of the first 5 even numbers.

The number series 2, 4, 6, 8, 10, 12, . . . . , 20. Therefore, 110 is the sum of first 10 even numbers.

There are 50 odd numbers from 1 to 100. Avaregae sum = 50.

From this sum, we can say that n=100, a=2 and d=2. So, we can say that the sum of the first 100 even integers is equal to 10100.