Ask questions and get helpful answers.

The sum of 16th term of an Ap is 240 and the next 4 terms is 220. Find the first term, common difference.

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩

4 answers

  1. If your question means:

    The sum of 16th term of an Ap is 240 and the sum of next 4 terms is 220.

    then

    Sum of first n terms of an AP:

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

    In this case n = 16.

    S16 = 240

    16 ( 2 a + 15 d ) / 2 = 240

    Multiply both sides by 2

    16 ( 2 a + 15 d ) = 480

    Divide both sides by 16

    2 a + 15 d = 30

    In AP

    an = a + ( n - 1 ) d

    a17 = a + 16 d

    a18 = a + 17 d

    a19 = a + 18 d

    a20 = a + 19 d

    The sum of next 4 terms:

    a17 + a18 + a19 + a20 = 220

    a + 16 d + a + 17 d + a + 18 d + a + 19 d = 220

    4 a + 70 d = 220

    Now you must solve system:

    2 a + 15 d = 30

    4 a + 70 d = 220

    The solution is:

    a = - 15 , d = 4

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  2. Of course:

    a = first term

    d = common difference.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  3. sum of 16 terms is 240
    8(2a + 15d) = 240
    2a + 15d = 30

    sum of 20 terms is 460 , (the first 240 plus the next 4 of 220 )
    10(2a + 19d) = 460
    2a + 19d = 46

    subtract them: 4d = 16
    d = 4
    sub into 2a+15d = 30
    2a + 60 = 30
    a = -15

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  4. Yes

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Answer this Question

Related Questions

Still need help?

You can ask a new question or browse existing questions.