Arithmetic progression

In some AP applies:

5a2 + 7a5 = 90
s3 = 12

Find the first member a =? and difference d = ?

Result

a =  2
d =  2

Solution:


5*(a+d)+7*(a+4*d) = 90
a+(a+d)+(a+2*d) = 12

12a+33d = 90
3a+3d = 12

a = 2
d = 2

Calculated by our linear equations calculator.








Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Do you have a system of equations and looking for calculator system of linear equations?

Next similar examples:

  1. AP - basics
    ap Determine first member and differentiate of the the following sequence: a3-a5=24 a4-2a5=61
  2. Sequence
    a_sequence Write the first 7 members of an arithmetic sequence: a1=-3, d=6.
  3. Sequence
    seq_1 Write the first 6 members of these sequence: a1 = 5 a2 = 7 an+2 = an+1 +2 an
  4. Sequence 2
    seq2 Write the first 5 members of an arithmetic sequence a11=-14, d=-1
  5. Sequence 3
    75 Write the first 5 members of an arithmetic sequence: a4=-35, a11=-105.
  6. Seats
    divadlo_2 Seats in the sport hall are organized so that each subsequent row has five more seats. First has 10 seats. How many seats are: a) in the eighth row b) in the eighteenth row
  7. AP - simple
    sigma_1 Determine the first nine elements of sequence if a10 = -1 and d = 4
  8. AP 6
    progression_ao Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38
  9. Fifth member
    arithmet_seq_1 Determine the fifth member of the arithmetic progression, if the sum of the second and fifth members equal to 73, and difference d = 7.
  10. Third member
    seq_6 Determine the third member of the AP if a4=93, d=7.5.
  11. AS sequence
    AP In an arithmetic sequence is given the difference d = -3 and a71 = 455. a) Determine the value of a62 b) Determine the sum of 71 members.
  12. Determine AP
    diff Determine the difference of the arithmetic progression if a3 = 7, and a4 + a5 = 71
  13. Three workshops
    workers_24 There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
  14. Theorem prove
    thales_1 We want to prove the sentense: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  15. Ball game
    lopta_3 Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
  16. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  17. Elimination method
    rovnice_1 Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15