# Algebra-Progressions

solution The sum of the squares of two positive integers is 208.If the square of the larger number is 18 times the smaller number,find the numbers.

solution The sum of the first n natural numbers is 276.Find the value of n.

solution There are three consecutive positive integers such that the sum of the square of the first and the product of the other two is 154.What are the integers?

solution The sum of the first n even natural numbers is given by the relation $S=n(n+1)\,$.Find n, if the sum is 420.

solution Find two consecutive odd natural numbers the sum of whose squares is 202.

solution Determine two consecutive even positive integers,the sum of whose squares is 100.

solution The sum of the two natural numbers is 8.Determine the numbers,if the sum of their reciprocals is ${\frac {8}{15}}\,$

solution The first term of an Arithmetic Progression (A.P) is $-2\,$ and the 10th term is $16\,$.Determine the 15th term.

solution The 8th term of an A.P is 17 and the 19th term is $39\,$.Find the 25th term.

solution Determine $k\,$ so that $k+2,4k-6,3k-2\,$ are the three consecutive terms of an A.P

solution How many terms of an A.P $1,4,7,.......\,$ are needed to make the sum 715?

solution Find the sum of all natural numbers between $1\,$ and $100\,$ which are multiples of $3\,$

solution The sum of first three terms of an A.P is $36\,$ while their product is $1620\,$.Find the A.P.

solution Find the sum of the first 24 terms of the sequence whose nth term is given by $a_{n}=3+{\frac {2}{3}}n\,$

solution Find the sum of the squares of the first $n\,$ natural numbers $1,2,3,4.........\,$

solution Find the sum of the cubes of the first $n\,$ natural numbers.

solution Find the sum to $n\,$ terms of the series $1\cdot 3+3\cdot 5+5\cdot 7+........\,$

solution Which term of the Geometric Progression(G.P) $2,2{\sqrt {2}},4......\,$ is $64\,$

solution Three numbers are in G.P.Their sum is $21\,$ and their product is $216\,$.Find them.

solution Insert $5\,$ geometric means between ${\frac {1}{3}}\,$ and $243\,$

solution If the Arithmetic mean(A.M) and Geometric Mean (G.M) of two numbers are $13,12\,$ respectively.Find the numbers.

solution Find the sum of the following sequence to $n\,$ terms.

$9,99,999,........(n9's)\,$.

solution Find the sum of the $n\,$ terms of the series $0.5+0.55+0.555+.......n\,$terms.

solution If the mth,nth and pth terms of a G.P form three consecutive terms fo a geometric sequence,prove that $m,n,p\,$ form three consecutive terms of an arithmetic sequence.

solution The sum of the first three terms of a GP is ${\frac {39}{10}}\,$ and their product is $1\,$.Find the terms.

solution How many terms of a GP $3,3^{2},3^{3},........\,$ are needed to give teh sum $120\,$

solution Insert 4 harmonic means between ${\frac {1}{12}}\,$ and ${\frac {1}{42}}\,$