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 + x2 + x3 + ... + xn-1 ----------------------------------------- 1 + x2 + x4 + x6 + ... + x2n-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 = 3x2 .|
The numbers a, a', a" constitute an arithmetic sequence and b,b',b" form a geometric sequence.
Calculate the ratio of the geometric sequence.
if a,b,c form an arithmetic sequence, then
b2 + bc + c2, c2 + ca + a2, a2 + ab + b2 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 + 2.52+ 3.52+ ... + n.5n= (5 + (4n-1)5n+1)/16
u1, u2, u3, ... is an arithmetic sequence and u2 - u1 = v|
S1 = u1 + u2 + ... + u9 + u10
S2 = u11 + u12 + ... + u19 + u20
S3 = u21 + u22 + ... + u29 + u30
Show that the sequence S1, S2, S3, ... 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.
x4 - (3m + 1) x2 + m2 = 0 (1)
In a sequence is the sum of the first n terms = sn = 2n.p - 1,
with p = a fixed real number.
Show that the sequence is geometric.