find the sum of all even number from 1 to 350
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Let the first even number between 1 to 350 be 2. Then
2, 4, 6, ....., 350
Here,
a = 2
d = 2
l = 350
Tn = l
=> l = a + (n - 1)d => 350 = 2 + (n-1)2
=> 350 - 2 = 2(n-1)
=> 348/2 = n-1
=> 174 = n - 1 => n = 174 + 1 = 175
Sum = n/2 (a + l) = 175/2 ( 2 + 350 )
= 175/2 × 352 = 175 × 176 = 30,800
2, 4, 6, ....., 350
Here,
a = 2
d = 2
l = 350
Tn = l
=> l = a + (n - 1)d => 350 = 2 + (n-1)2
=> 350 - 2 = 2(n-1)
=> 348/2 = n-1
=> 174 = n - 1 => n = 174 + 1 = 175
Sum = n/2 (a + l) = 175/2 ( 2 + 350 )
= 175/2 × 352 = 175 × 176 = 30,800
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