Multiple choice

A sequence consists of 50 terms and follows an arithmetic progression. The fourth term of the sequence is 10. It is also known that twice the fifth term plus three times the eighth term is equal to the sum of the tenth and fifteenth terms. What is the sum of all the terms of the sequence?

  1. 10,350

  2. 12,250

  3. 11,200

  4. 11,250
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D Correct answer
Explanation

a + 3d = 10. 2(a+4d) + 3(a+7d) = (a+9d) + (a+14d). 2a + 8d + 3a + 21d = 2a + 23d. 3a = -6d, so a = -2d. Substitute into first: -2d + 3d = 10, so d = 10, a = -20. Sum = (n/2) * (2a + (n-1)d) = 25 * (-40 + 49*10) = 25 * 450 = 11250.

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