Question

If first, second and eighth terms of a G.P.
are respectively ně4, n", n52, then the
value of nis​

Answer 1

The GP series can be written as a,ar,ar²,ar3....ar3...., where a is the first term and r commom multiple .

So it is given the first term is n−4n−4, i.e a=n−4.n−4.

Also given second term i.e ar=nn.nn.

So now divide second by first, you get the value of r= ara=nnn−4=n(n+4)ara=nnn−4=n(n+4)

Then, it is given as 8 th term i.e, ar7=n52ar7=n52 which means

(n−4)(nn+4)7=n52(n−4)(nn+4)7=n52

⟹(n−4)(n(7n+28))=n52⟹(n−4)(n(7n+28))=n52

⟹n(7n+24)=n52⟹n(7n+24)=n52

Apply the laws of exponential! Since base are equal, powers must be equal. Hence,

7n+24=52⟹7n=287n+24=52⟹7n=28

∴∴ n=4.

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