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LoginInterview Questions Math 1 year ago
Posted on 18 Jan 2024, this text provides information on Math related to Interview Questions. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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RiaElidaMF RiaElidaMF
Best Answer
1 year ago
rithmetic means A1, A2, A3, A4, A5, As are inserted between two consecutive natural number and b (a > b). If A12 - A22 + A32 - A1+ As2 - As? is EQUAL to prime number then 'b' is equal toGiven,6 Arithmetic means A1, A2, A3, A4, A5, A6If N AMs are inserted between two numbers a and b, then we have common difference,d = ( b - a ) / (N + 1)as N = 6, we have,d = ( b - a ) / (6 + 1)d = ( b - a ) / 7Now consider,A1² - A2² + A3² - A4²+ A5² - A6²= (A1 + A2) (A1 - A2) + (A3 + A4) (A3 - A4) + (A5 + A6) (A5 - A6) = (A1 + A2) (-d) + (A3 + A4) (-d) + (A5 + A6) (-d) = (-d) (A1 + A2 + A3 + A4 + A5 + A6)as we know that,A1 = a + dA2 = a + 2dA3 = a + 3dA4 = a + 4dA5 = a + 5dA6 = a + 6d= (-d) (a + d + a + 2d + a + 3d + a + 4d + a + 5d + a + 6d)= (-d) (6a + 21d)= - ( b - a ) / 7 [ 6a + 21 ( b - a ) / 7 ]= (a - b)/7 (21a + 21b)/7= (a - b)/7 × 3(a + b)= 3/7 (a - b) (a + b)= 3/7 (a² - b²)Given 3/7 (a² - b²) is a prime number This is POSSIBLE only when, (a² - b²) = 7 Given a and b are consecutive numbers and a > b. Therefore, a = b + 1using the above equation, we GET, (a² - b²) = 7 (b+1)² - b² = 7b² + 1 + 2b - b² = 71 + 2b = 72b = 6b = 3Therefore the values of a and b are a = b + 1 = 3 + 1 = 4 and b = 3∴ a = 4, b = 3
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