# AP 6

Calculate the first five items of an arithmetic sequence if it is given:
a2 – a3 + a5 = 20
a1 + a6 = 38

Result

a =  14
a2 =  16
a3 =  18
a4 =  20
a5 =  22

#### Solution:

(a+d) – (a+2d) + (a+4d) = 20
a + (a+5d) = 38

a+3d = 20
2a+5d = 38

a = 14
d = 2

Calculated by our linear equations calculator.
$a_{2}=a+d=16$
$a_{3}=a_{2}+d=18$
$a_{4}=a_{3}+d=20$
$a_{5}=a_{4}+d=22$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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

Be the first to comment!

Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

## Next similar math problems:

1. AP - basics
Determine first member and differentiate of the the following sequence: a3-a5=24 a4-2a5=61
2. Sequence 2
Write the first 5 members of an arithmetic sequence a11=-14, d=-1
3. Sequence
Write the first 6 members of these sequence: a1 = 5 a2 = 7 an+2 = an+1 +2 an
4. Sequence 3
Write the first 5 members of an arithmetic sequence: a4=-35, a11=-105.
5. AP - simple
Determine the first nine elements of sequence if a10 = -1 and d = 4
6. Three workshops
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?
7. Stones 3
Simiyu and Nasike each collected a number of stones in an arithmetic lesson. If Simiyu gave Nasike 5 stones, Nasike would have twice as many stones as Simiyu. If initially, Simiyu had five stones less than Nasike how many stones did each have?
8. AS sequence
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.
9. Sequence
Between numbers 1 and 53 insert n members of the arithmetic sequence that its sum is 702.
10. Children
The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group?
11. Ball game
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.
12. Three unknowns
Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0
13. Legs
Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
14. Guppies for sale
Paul had a bowl of guppies for sale. Four customers were milling around the store. 1. Rod told paul - I'll take half the guppies in the bowl, plus had a guppy. 2. Heather said - I'll take half of what you have, plus half a guppy. The third customer, Na
15. Linsys2
Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
16. Elimination method
Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
17. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?