Sequences and Series
(x−4) is geometric mean of (x−5) and (x−2) find x.
Geometric mean of two numbers, a and b is abSo, geometric mean of (x−5),(x−2) is (x−5)×(x−2)=(x−4)
Squaring both sides,
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If the sum of n terms of an A.P. is 3n2+5n and its mth term is 164, find the value of m.
For what value of x, the number −72,x,−72are in G.P.?
A fanner buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?
The sum of n
terms of two arithmetic progressions are in the ratio (3n+8):(7n+15)˙
Find the ratio of their 12th terms.
Find the sum to n terms of the series :12+(12+22)+(12+22+32)+˙˙˙
The sum of three numbers m GP is 56. If we subtract 1.7,21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.
Show that the products of the corresponding terms of the sequences a, ar,ar2,,˙˙˙arn−1and A,AR,AR2,,˙˙˙ARn−1,form a G.P, and find the common ratio.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.