Mathematics

Question

Write the sum using summation notation, assuming the suggested pattern continues. -10 - 2 + 6 + 14 + ... + 110

2 Answer

  • This is the sum of the arithmetic sequence:
     10 - 2 + 6 + 14 + ... + 110
    where:  a 1 = - 10, d = 8
    a n = 110
    a n = a 1 + ( n - 1 ) * d
    110 = - 10 + ( n - 1 ) * 8
    110 = - 10 + 8 n - 8
    110 + 10 + 8 = 8 n
    128 = 8 n
    n = 128 : 8
    n = 16
    ∑ n = n/2 * ( a 1 + a n ) 
    ∑ 16 = 16/2 * ( -10 + 110 ) = 8 * 100 = 800
    Answer:
    The sum is 800.
  • The answer is  summation of the quantity negative ten plus eight n from n equals zero to fifteen

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