Question

Find the sum of the first 100 positive odd integers

Answer 1

Answer:

step 1 Address the formula, input parameters & values.

Input parameters & values:

The number series 1, 3, 5, 7, 9, . . . . , 199.

The first term a = 1

The common difference d = 2

Total number of terms n = 100

step 2 apply the input parameter values in the AP formula

Sum = n/2 x (a + Tn)

= 100/2 x (1 + 199)

= (100 x 200)/ 2

= 20000/2

1 + 3 + 5 + 7 + 9 + . . . . + 199 = 10000

Therefore, 10000 is the sum of first 100 odd numbers.

Step-by-step explanation:

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Answer 2

SOLUTION

TO DETERMINE

The sum of the first 100 positive odd integers

EVALUATION

The set of positive odd integers are

1 , 3 , 5 , 7 , 9 , 11 ,....

First term = a = 1

Common Difference = d = 3 - 1 = 2

Number of terms = 100

Hence the required sum

$\displaystyle \sf{ = \frac{100}{2} \bigg[2a + (n - 1)d \bigg] }$

$\displaystyle \sf{ = \frac{100}{2} \bigg[(2 \times 1)+ (100 - 1) \times 2\bigg] }$

$\displaystyle \sf{ = \frac{100}{2} \bigg[2+ 198\bigg] }$

$\displaystyle \sf{ = 50 \times 200}$

$\displaystyle \sf{ =10000 }$

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