soni_pallavi wrote:Q1) A special sequence of numbers is written as 2,9,28,65,126...Find the ratio of the 7th term to the 15th term??
a)1/4
b)1/2
c)129/422
d)43/422
e)43/129
Answer D
The formula for the sequence seems to be:
S(n) = n³ + 1.
To illustrate:
S(1) = 1³ + 1 = 2.
S(2) = 2³ + 1 = 9.
And so on.
Thus: S(7) = 7³ + 1 and S(15) = 15³ + 1.
A helpful identity:
a³ + b³ = (a+b)(a²-ab+b²)
Thus:
S(7) / S(15) =
= (7³ + 1³)/(15³ + 1³)
= (7+1)(7² - 7*1 + 1²) / (15+1)(15² - 15*1 + 1²)
= 8*43 / 16*211
= 43/422.
The correct answer is
D.
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