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Sequences & Series: Level 3 1. The sum of the squares of the first 10 positive integers (\(1^2 + 2^2 + … + 10^2\)) is 385. What is the value of the series \((1^2 + 1) + (2^2 + 2) + … + (10^2 + 10)\)? 395 400 435 440 450 Check Solution (D): 1….
Sequences & Series: Level 2 1. The sum of the squares of the first 10 positive integers (\(1^2 + … + 10^2\)) is 385. What is the sum of the squares of the first 10 positive even integers (\(2^2 + 4^2 + … + 20^2\))? 385 770 1155 1540 3850 Check Solution (D): The sum…
Progressions — Concept Explanation A progression is an ordered sequence of numbers following a definite pattern or rule. The most common progressions are: Natural-number series (simple summation patterns) Arithmetic Progression (A.P.) – constant difference Geometric Progression (G.P.) – constant ratio Each has its own formula for the nth term and for the sum of terms….
Sequences & Series: Level 1 1. The first term in a sequence is 3, and each subsequent term is 4 more than the term before it. What is the value of the 11th term? 34 40 43 47 51 Check Solution (C): This is an arithmetic sequence with \(a_1 = 3\) and \(d = 4\)….
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