Sequences and Series
Find the 3 Arithmetic Means between 18 and 30
The primary arithmetic mean between 18 and 30
Arithmetic mean between initial value and midpoint is
Arithmetic mean between final value and midpoint is
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Find the sum of the series 313+323++503˙
If the arithmetic progression whose common difference is nonzero the sum of first 3n
terms is equal to the sum of next n
terms. Then, find the ratio of the sum of the 2n
terms to the sum of next 2n
Find the sum to n
terms of the series 1×2×3+2×3×4+3×4×5+˙
Divide 32 into four parts which are in A.P. such that the ratio of the product of extremes to the product of means is 7:15.
are in A.P. and x,2,andz
are in G.P., then prove that x,and4,z
are in H.P.
are in H.P., then prove that (b+c+d)/a,(c+d+a)/b,(d+a+b)/c
, are in A.P.
If the sum of the squares of the first n
natural numbers exceeds theri sum by 330,
Prove that (6666)2+(8888)=44444.