Math

posted by .

In an A.P.the third term is 4 times the first term and the 6th term is 17. Find the series

  • Math -

    If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:

    an = a1 + ( n - 1 ) * d


    a3 = a1 + ( 3 - 1 ) * d

    a3 = a1 + 2 d


    a3 = 4 a1

    4 a1 = a1 + 2 d

    4 a1 - a1 = 2d

    3 a1 = 2 d Divide both sides with 2

    3 a1 / 2 = d

    d = 3 a1 / 2


    an = a1 + ( n - 1 ) * d


    a6 = a1 + ( 6 - 1 ) * d = 17

    17 = a1 + 5 d

    17 = a1 + 5 * 3 a1 / 2

    17 = a1 + 15 a1 / 2

    17 = 2 a1 / 2 + 15 a1 / 2

    17 = 17 a1 / 2 Multiply both sides with 2

    34 = 17 a1 Divide both sides with 17

    34 / 17 = a1

    2 = a1

    a1 = 2


    d = 3 a1 / 2

    d = 3 * 2 / 2

    d = 6 / 2

    d = 3


    a1 = 2 , d = 3


    A.P.

    2 , 5 , 8 , 11 , 14 , 17 , 20 , 23 ...

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    The sum of the first seventeen terms of an arithmetic series is 493 The third term is 11. Find the first term and the seventeenth term. The n-th term is 3*n + 2
  2. Math

    3,5,-5... The first term in the sequence of #'s shown above is 3. Each even # term is 2 more than the previous term and each odd # term, after the first, is -1 times the previous term. For example, the second term is 3+2, and the third …
  3. Math

    The fifth term of an arithmetic progression is three times the second term,and the third term is 10.a)What is the first term,b)the common difference and c)the 15th term?
  4. math

    the fourth term of an arithmetic progression is equal to 3 times the first term and the seventh term exceeds twice the third term by 1 find the first term and the common differrence
  5. math

    The third term of a geometric progressiom is nine times the first term.if the second term is one-twenty fourth the fifth term.find the fourth term.ar^2=9a. r=sqr of 9 r=3.pls teach me how to get the first term and i can get the 4th …
  6. math

    if 4th term of an arithmetic progression is 3 times the 1st term nd 7th term exceeds twice the third term by 1. find the first term and common difference
  7. Arithmetic progession

    The third term of an A.P is 10times more than the second term. Find the sum of the eight and fifteen term of the A.P if the seventh term is seven times the first term
  8. Maths

    The sixth term of GP is 16 and the third term is 2.Find the first term and common ratio. 6th term =16 3rd term=2 So ar^5=16 and ar^2=2, then divide. So r^3=8, and r^3 =2^3. Therefore r =2 and a=1/2
  9. math

    If third term of an A.P. is four times of first term and sixth term is 17. find the series.
  10. Math

    In an A.P.the third term is four times the first term, and the sixth term is 17; find the series.

More Similar Questions