Arithmetic progression - problems
- Sum of inner angles
Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.
Show that if x, y, z are 3 consecutive nonzero digits, zyx-xyz = 198, where zyx and xyz are three-digit numbers created from x, y, z.
- The sum 2
The sum of five consecutive even integers is 150. Find the largest of the five integers. A.28 B.30 C.34 D.54 Show your solution and explain your answer.
Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
The tale of the Seven Ravens were seven brothers, each of whom was born exactly 2.5 years after the previous one. When the eldest of the brothers was 2-times older than the youngest, mother all curse. How old was seven ravens brothers when their mother cur
- Octahedron - sum
On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also.
Gabo draw n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon?
In the arithmetic sequence is a1=-1, d=4. Which member is equal to the number 203?
Mailbox is opening at regular intervals 3 times a day. The first time is opened at 8:00 and the last at 19:00. Calculate hours when mailbox is opened during day.
- AVG of INT
What is the average of the integers from 9 throuht 52 inclusive?
Cinema auditorium is built for 3300 people. The first row is planned for 36 seats and each next gradually 4 more. How many rows of seats will have auditorium?
In how many points will intersect 14 different lines, where no two are parallel?
- Angles in a triangle
The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=60°. What sizes have other angles in a triangle?
Andrew wrote this series of numbers: 1,3,7,15, .... n. Which number in the series does not belong? ?
In the arithmetic sequence is given: Sn=2304, d=2, an=95 Calculate a1 and n.
Help little C.F. Gauss sum all the integers from 1 to 420.
- Workman - shift
The worker produces 300 components per shift. How many components would be produced in 18 shift, if his performance gradually increased every shift by 3 components?
Write the first 7 members of an arithmetic sequence: a1=-3, d=6.
How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)?
- Sequence 2
Write the first 5 members of an arithmetic sequence a11=-14, d=-1