# Arithmetic progression - examples

- Sum of inner angles

Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees. - Digits

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. - Numbers

Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum? - Ravens

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. - n-gon

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? - Sequence

In the arithmetic sequence is a_{1}=-1, d=4. Which member is equal to the number 203? - Mailbox

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

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? - Lines

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? - Series

Andrew wrote this series of numbers: 1,3,7,15, .... n. Which number in the series does not belong? ? - Sequence

In the arithmetic sequence is given: S_{n}=2304, d=2, a_{n}=95 Calculate a_{1}and n. - Gauss

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? - Sequence

Write the first 7 members of an arithmetic sequence: a_{1}=-3, d=6. - Rope

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 a_{11}=-14, d=-1 - Angle in RT

Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions.

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