Find the sum of the first 25 terms of an arithmetic sequence whose first term is -9 and whose common difference is 5.?

5 Answers

Relevance
  • 6 months ago

    For an arithmetic sequence:

    a₁ = - 9

    a₂ = a₁ + d ← where d is the common difference, i.e.: 5

    a₃ = a₂ + d = a₁ + 2d

    a₃ = a₃ + d = a₁ + 3d

    …and you can generalize writing:

    a(n) = a₁ + (n - 1).d → for the 25th term, n = 25

    a₂₅ = - 9 + (25 - 1).5

    a₂₅ = - 9 + 120

    a₂₅ = 111

    s = a₁ + a₂ + a₃ + a₃ + … + a₂₅

    s = (- 9) + (- 4) + (1) + (6) + … + (111)

    s = (111) + (106) + (101) + (96) + … + (- 9)

    2s = (102) * 25

    s = 51 * 25

    s = 1275

  • 6 months ago

    -9, -4, 1, 6, ...

    an = 5 n - 14

    S25 = (25/2)(-9 + 111) = 5100/4 = 1275

  • T[1] = -9 = -14 + 5 * 1

    T[n] = -14 + 5 * n

    T[25] = -14 + 5 * 25 = 125 - 14 = 111

    S[n] = (n/2) * (T[1] + T[n])

    S[25] = (25/2) * (-9 + 111)

    S[25] = (25/2) * (102)

    S[25] = 25 * 51

    S[25] = 25 * 50 + 25 * 1

    S[25] = 1250 + 25

    S[25] = 1275

  • 6 months ago

    Apply the formula

    Sum to n terms of an AP =

    (n/2)*[2a + (n - 1)d]

    where n = number of terms = 25

    a is first term = -9

    d is common difference = 5

    Ans: 1275

  • How do you think about the answers? You can sign in to vote the answer.
  • 6 months ago

    S_n = n*a + d*(n-1)*n/2

    25 * -9 + 5 * 24 * 25 / 2 = 1275

Still have questions? Get your answers by asking now.