Question 20 What is the sum of all the natural numbers from 91 to 200?
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Question 20
What is the sum of all the natural numbers from 91 to 200?
Show answer & explanation
Using the arithmetic series formula, the sum of consecutive integers from a to b is n(a+b)/2, where n is the count of terms. From 91 to 200, there are 110 terms (200 - 91 + 1). The sum is 110 × (91 + 200) / 2 = 110 × 291 / 2 = 20100.
Step-by-step Derivation:
Step 1: Identify the sequence: 91, 92, 93, ..., 200 (arithmetic series with first term a=91, last term l=200)
Step 2: Count the terms: n = 200 - 91 + 1 = 110
Step 3: Apply arithmetic series sum formula: S = n(a + l)/2
Step 4: Calculate: S = 110(91 + 200)/2 = 110 × 291/2 = 32010/2 = 20100
Step 5: Verify: Average = (91 + 200)/2 = 145.5; Sum = 145.5 × 110 = 20100 ✓