find the sum of first 15 natural numbers
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Step-by-step explanation:
step 1 address the formula, input parameters & values.
Input parameters & values:
The number series 1, 2, 3, 4, . . . . , 14, 15.
The first term a = 1
The common difference d = 1
Total number of terms n = 15
step 2 apply the input parameter values in the formula
Sum = n/2 x (a + Tn)
= 15/2 x (1 + 15)
= 240/2
1 + 2 + 3 + 4 + . . . . + 14 + 15 = 120
Therefore, 120 is the sum of positive integers upto 15.
SOLUTION
TO DETERMINE
The sum of first 15 natural numbers
EVALUATION
Here first 15 natural numbers are
1 , 2 , 3 , 4 , . . . . , 15
This is an arithmetic progression
First term = a = 1
Common Difference = d = 1
Number of terms = 15
Hence the required sum
[tex]\displaystyle \sf{ = \frac{n}{2} \bigg[ 2a + (n - 1)d\bigg] }[/tex]
[tex]\displaystyle \sf{ = \frac{15}{2} \bigg[ (2 \times 1) + (15 - 1)\bigg] }[/tex]
[tex]\displaystyle \sf{ = \frac{15}{2} \bigg[ 2 + 14\bigg] }[/tex]
[tex]\displaystyle \sf{ = \frac{15}{2} \times 16 }[/tex]
[tex]\displaystyle \sf{ = 15 \times 8}[/tex]
[tex]\displaystyle \sf{ = 120 }[/tex]
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