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The sum all even natural numbers between 1 and 31 is:


Options:
A .  16
B .  128
C .  240
D .  512
Answer: Option C

Required sum = (2 + 4 + 6 + ... + 30)

This is an A.P. in which a = 2, d = (4 - 2) = 2 and l = 30.

Let the number of terms be n. Then,

tn = 30 The Sum All Even Natural Numbers Between 1 And 31 Is:    a + (n - 1)d = 30

The Sum All Even Natural Numbers Between 1 And 31 Is: 2 + (n - 1) x 2 = 30

The Sum All Even Natural Numbers Between 1 And 31 Is: n - 1 = 14

The Sum All Even Natural Numbers Between 1 And 31 Is: n = 15

The Sum All Even Natural Numbers Between 1 And 31 Is: Sn = n (a + l) = 15 x (2 + 30)   = 240. 2 2


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