maths

the sum of 3rd and 5th terms of an a.p is 38 and sum of 7th and 10th terms of an a.p is 83,find the a.p.
please help all questions please help please.

  1. 👍 0
  2. 👎 0
  3. 👁 506
  1. We have the formula a+(n-1)d=nth term
    Where a is the 1st term ,d is the difference and n is the nth term
    So1st term= a
    2nd term= (a+1)d
    3rd term= (a+2)d
    5th term=(a+4)d
    Adding ad+2d+ad+ 4d= 38
    2ad+ 6d= 38
    In the same way 7th term=(a+6)d
    10th term=(a+9)d
    Adding these 2ad+15d=83
    Subtracting, 9d= 45 which makes d=5

    1. 👍 0
    2. 👎 2
  2. a+2d + a+4d=38 -->2a + 6d = 38
    a+6d + a+9d = 83 --> 2a + 15d = 83

    subtract them:
    9d = 45
    d=5

    back in 2a+6d = 38
    2a+30=38
    a=4

    the sequence is:

    4 9 14 19 24 ...

    BTW, the definitions used by Praphul are not correct.
    e.g. he said:
    5th term is (a+4)d
    that should have been a + 4d, the brackets there are critical

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. maths

    the sum of the 4th and 6th terms of an A.P is 42. the sum of the 3rd and 9th terms of the progression is 52. find the first term, the common difference and the sum of the first ten terms of the progression.

  2. math

    The sum of the 1st nine terms of an arithmetic series is 216. The 1st,3rd and the 7th terms of series form the 1st three terms of a geometric series. Find the 1st term and the constant difference of the arithmetic series ?

  3. Maths

    The sum of 1st five terms of an AP nd the sum of the 1st seven termd of the same AP is 167. If the sum of the 1st ten terms of this AP is 235, find the sum of its1st twenty terms

  4. Math

    In an arithmetic series, the sum of the 5th to the 8th terms inclusive is 114, whilst the sum of the 12th to 15th terms inclusive is 198. What is the 21st term? I have got 99=2a +3d and 57= 2a+3d Im not sure what to do now

  1. maths

    the sum of the first nine terms of an arithmetic sequence 216. The 1st, 3rd and 7th terms form the first three terms of a geometric sequence therefore find the common difference

  2. mathematics

    1} the first term of an AP is 2 and the common difference is 3.Find the sum of the first 11 terms. 2}The 2nd and 5th terms of a GP are -6 and 48 respectively.Find the sum of the first four terms

  3. ap

    in an AP, if the 5th and 12th terms are 30 and 65 respectively. what is the sum of first 20terms

  4. Math

    The 3rd and 9th term of a g.p are 54 and 39,336 respectively.find the 6th term,sum of 4th term,sum of 4th and 7th term and product of 2nd and 5th term

  1. arithmetic

    THE SUM OF THE 2ND AND 5TH TERMS OF AN A.P IS 42. IF THE DIFFERENCE BETWEEN THE 6TH AND 3RD TERM IS 12, FIND THE: COMMON DIFFERENCE, 1ST TERM, 20TH TERM.

  2. maths

    In an arithmatic sequence, sum of 9 terms is 279 and sum of 20 terms is 1280. Find 5th term ? Find 16th term ? Write the sequence.

  3. Mathematics

    If the 2nd and 5th term of a g.p are -6 and 48 respectively.Find the sum of the first four terms

  4. world issuse

    I'm a 7 letter word u read daily,my 5th 6th and 7th letter increase each year,my 3rd n 4th letter are the same,my 3rd 2nd n 5th letter cover 75% of the world.

You can view more similar questions or ask a new question.