In-the-arithmetic-progression-u-1-1-Given-that-u-7-u-11-and-u-17-are-in-geometric-progression-find-the-value-of-each-

Question Number 11256 by 786786AM last updated on 18/Mar/17

In the arithmetic progression, u_{1} = 1 . Given that u_{7}, u_{11} and u_{17} are in geometric

progression, find the value of each .

Answered by ajfour last updated on 18/Mar/17

n_{7} = 1 + 6 d

n_{11} = 1 + 10 d

n_{17} = 1 + 16 d

as {(n_{11})}^{2} = n_{7} n_{17}

{(1 + 10 d)}^{2} = (1 + 6 d) (1 + 16 d)

1 + 20 d + {100 d}^{2} = 1 + 22 d + {96 d}^{2}

if d \neq 0, then 4 d = 2

d = \frac{1}{2}

n_{7} = 1 + 6 d = 4

n_{11} = 1 + 10 d = 6

n_{17} = 1 + 16 d = 9

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