If a problem is solved. It is not 'the' answer.
No attempt is made to search for the most elegant answer.
I highly recommend that you at least try to solve the
problem before you read the solution.
The angles of a rectangular triangle are the terms of an arithmetic sequence. Calculate these angles. |
In an arithmetic sequence is t(2) = 3.t(3) . The sum of n terms, starting from t(1), is 0. Calculate n. |
Calculate 1 + x + x^{2} + x^{3} + ... + x^{n-1} ----------------------------------------- 1 + x^{2} + x^{4} + x^{6} + ... + x^{2n-2} |
The sides of a triangle form a geometric sequence. What are the limits of the ratio. |
The points with coordinates (a,b) (a',b') (a",b") are points of a
parabola y = 3x^{2} . The numbers a, a', a" constitute an arithmetic sequence and b,b',b" form a geometric sequence. Calculate the ratio of the geometric sequence. |
Prove that: if a,b,c form an arithmetic sequence, then b^{2} + bc + c^{2}, c^{2} + ca + a^{2}, a^{2} + ab + b^{2} form an arithmetic sequence. |
An arithmetic sequence has terms t(1),t(2),t(3),... The first term t(1) = a and the common difference is v (not 0). The terms t(5),t(9) and t(16) form a three term geometric sequence with common ratio q. Calculate q. Calculate t(k) in terms of k and a. |
Prove that for each integer n > 0 1.5 + 2.5^{2}+ 3.5^{2}+ ... + n.5^{n}= (5 + (4n-1)5^{n+1})/16 |
u_{1}, u_{2}, u_{3}, ... is an arithmetic sequence and u_{2} - u_{1} = v S_{1} = u_{1} + u_{2} + ... + u_{9} + u_{10} S_{2} = u_{11} + u_{12} + ... + u_{19} + u_{20} S_{3} = u_{21} + u_{22} + ... + u_{29} + u_{30} etc ... Show that the sequence S_{1}, S_{2}, S_{3}, ... is an arithmetic sequence. |
Calculate the sum of the squares of the first n strictly positive integers. |
Calculate all m values such that the roots of the following equation
constitute an arithmetic sequence.
x^{4} - (3m + 1) x^{2} + m^{2} = 0 (1) |
In a sequence is the sum of the first n terms = s_{n} = 2^{n.p} - 1,
with p = a fixed real number.
Show that the sequence is geometric. |