Sequences and Series
Write the quadratic equation, the arithmetic and geometric means of whose roots are A and G respectively.
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Let the sequence anbe defined as follows : a1=1,an=an−1+2for n≥2. Find first five terms and write corresponding series.
The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.
Find the sum to n terms of the sequence, 8, 88, 888, 8888 . . . .
Write the first five terms of the sequence whose nthterms are : an=n4n2+5
Which term of the G.P., 2, 8, 32, . . . up to n terms in 131072?
In an AP: given a=8,an=62,Sn=210 find n and d
A manufacturer reckons that the value of a machine, which costs him Rs. 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.