Task 1 · easy
General formula expression
The string a_n=3n-2 is given. Calculate a_10.
Hint and solution →Original practice tasks · Math · High school . Class 2
Strings — tasks with solutions
Start with the easier exercises and work your way up. Every task has a hint and a full step-by-step solution — try it on your own first, then unlock the solution and compare.
Easy
7
Medium
8
Hard
5
Task 2 · easy
First words of string
The string a_n=n2-n for n≥1 is given. Give me the first four words.
Hint and solution →Task 3 · easy
Recursive string
The string a_1=2, a_ ((n+1) =a_n+3. Give me the first five words.
Hint and solution →Task 4 · medium
Stretch monotonics
Test monotonicity a_n=5-2n.
Hint and solution →Task 5 · easy
Arithmetic detection
Check if 4, 7, 10, 13 is an arithmetic sequence.
Hint and solution →Task 6 · easy
Non-arrhythmic string
See if 1, 2, 4, 7, ... is an arithmetic string.
Hint and solution →Task 7 · medium
N-th expression of arithmetical sequence
Within arithmetic a_1=5, r=-2. Calculate a_12.
Hint and solution →Task 8 · hard
Determination of a1 and r
Within arithmetic a_3=11 and a_8=31. Select a_1 and r.
Hint and solution →Task 9 · medium
Sum of arithmetical strings
The arithmetic string a_1=4, r=3. Calculate S_20.
Hint and solution →Task 10 · medium
Designation of the word number
Within arithmetic a_1=7, r=5. Which word is 52?
Hint and solution →Task 11 · easy
Meteorological signal recognition
See if 3, 6, 12, 24, ... is a geometrical sequence.
Hint and solution →Task 12 · medium
N-th expression of geometric string
In geometrical sequence a_1=81, q=1/3. Calculate a_5.
Hint and solution →Task 13 · hard
Determination of a1 and q
In geometrical sequence a_2=6 and a_5=162. Select the actual q and a_1.
Hint and solution →Task 14 · medium
Sum of geometric string
The geometric sequence a_1=5, q=2 is given. Calculate S_8.
Hint and solution →Task 15 · easy
Total at q=1
The geometric sequence a_1 = 7, q=1 is given. Calculate S_12.
Hint and solution →Task 16 · hard
Arithmetic model in practice
There are 18 places in the front row and 2 more in each row. How many places are in the 15th row and how many in the first 15 rows?
Hint and solution →Task 17 · medium
Geometric Growth Model
At first, there are 200 units. After each full period, the number of units is three times higher. What's after four periods?
Hint and solution →Task 18 · hard
Percentage folded as geometric string
The capital of PLN 4000 increases by 4% per year with annual capitalisation, without taxes and charges. Calculate the value after 3 years.
Hint and solution →Task 19 · medium
Other type of string
Check if the string 1, 4, 9, 16, ...is arithmetical or geometric.
Hint and solution →Task 20 · hard
The sum of the string parameter
Within arithmetic a_1=5 and S_20=860. Mark r.
Hint and solution →Karta pracy do druku
Ten sam temat w wersji na kartkę: instrukcja, zadania i miejsce na odpowiedzi. Wydruk jest bezpłatny.
Otwórz kartę pracy →After the tasks
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