The sum of the sequence: 2 + 4 + 6 + ..... + 98 + 100 = ____?
- 2450
- 2500
- 2550
- None of these
Explanation
This is an arithmetic sequence with first term a = 2, last term l = 100, and common difference d = 2.
Step 1: Find the number of terms (n)
The nth term of an arithmetic sequence is given by: l = a + (n - 1)d
100 = 2 + (n - 1)2
100 = 2 + 2n - 2
100 = 2n
n = 50
Step 2: Calculate the sum of the sequence
Sum = n/2 * (a + l)
= 50/2 * (2 + 100)
= 25 * 102
= 2550
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