Math, asked by arusa0, 1 year ago

Find the sum of first 123 even natural number

Answers

Answered by saurabhsemalti
11
even numbers are
2,4,6,...

treating it as AP with n =123 , a=2 and d=2.
a |n|  = a + (n - 1)d \\ a |n|  = 2 + (122)(2) \\ a |n|  = 246
now we know sum of AP
s |n|  =  \frac{n}{2} (a + l) \\  =  \frac{123}{2} (2 + 246) \\  = 123(1 + 123) \\  = 123 \times 124 \\  = 15252

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arusa0: 246 kaise aaya
saurabhsemalti: Jo a(n) calculate kiya hai vhi hai
arusa0: nhi samjha
arusa0: ager 122+2=144,144×2=288
arusa0: plz explain
arusa0: I'm understand
arusa0: thankx
arusa0: i cant understand last third step
Answered by BrainlyVirat
14
Here is the answer

2 , 4 , 6 ..., 2n are the even natural numbers.

Here ,
 \tt{a = t_{1} = 2}

 \tt{ t_{2} = 4}

 \tt{t_{3} = 6...}

 \tt{d = t_{2} - t_{1} = 4 - 2 = 2}
n = 123

 \tt {s_{n} = \frac{n}{2} (2a + (n - 1)d)}

\tt {= \frac{123}{2}(2 \times 2 +(123 - 1) \times 2)}

 \tt {= \frac{123}{2} (4 + 122 \times 2)}

 \tt { = \frac{123}{2} (4 + 248)}

 \frac{123}{2} \times 248


 \tt {= 123 \times 124}

 \tt {s_{123} = 15252}

The sum of the first 123 even natural numbers is 15252.
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