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i. What is the sum of first 20 natural numbers? ii. The algebraic form of an arithmetic sequence is 6n + 5. Find the sum of first 20 terms of this sequence? |
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Answer» i. Sum of first n natural numbers = n(n + 1)/2 ∴ Sum of first 20 natural numbers = 20 x (20 + 1)/2 = (20 x 21)/2 = 420 / 2 = 210 ii. The algebric form = 6n + 5 Common difference 'd' = coefficient of n = 6 First term 'x1' = (coefficient of n) + (constant term) = 6 + 5 = 11 Sum of first 20 terms = \(\frac{1}{2}\) an(n + 1) + nb = \(\frac{1}{2}\) x 6 x 20 x 21 + 20 x 5 = 3 x 20 x 21 + 100 = 1260 + 100 = 1360 |
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