Find out whether the given sequence is an arithmetic sequence. If so, find the first term and the difference of the arithmetic sequence and determine whether the sequence is increasing or decreasing :

Find the terms *a _{2}*,

*a*and

_{5}*a*of the arithmetic sequence if you know :

_{7}

Find the sum *s _{5}*,

*s*and

_{12}*s*of the arithmetic sequence if you know :

_{20}

We put a few numbers between numbers 12 and 48 so that all the numbers together now form the increasing finite arithmetic sequence. The sum of all entered numbers is 330. What is the difference of the arithmetic sequence ?

Put 7 numbers between the numbers 3 and 43 so that they all together form an arithmetic sequence. What are the numbers ?

Lengths of the sides of a right-angled triangle are three consecutive terms of an arithmetic sequence. Calculate the length of the sides, if you know :**a)** perimeter of the triangle is 72 cm**b)** area of the triangle is 54 cm^{2}

Find the sum of**a)** the first *n* consecutive odd numbers**b)** the first *n* consecutive even numbers

Excavation of the first meter of the well costs 10 €. Each meter is more expensive by 2 €. Find the formula for dependency of the price *p* for digging the well on its depth *d* in meters.

In the cinema with a capacity of 1,656 people is 105 seats in the last row. How many rows are in the cinema, if in each lower row is always 3 seats less than in the previous row ?

The student needs to study 313 pages of math textbook for an exam he has in 14 days. If the first day he studied 35 pages and each following day he studied two pages less than the previous day, how many pages will he have to handle during the day before the exam ?

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