Question

for a G.P the ratio of the 7th and 3rd term is 16. the sum of a term is 2555. what is first term​

Answer 1

Step-by-step explanation:

hope attached photo helps you

Answer 2

Answer:

The first term of the geometric progression is 5

Step-by-step explanation:

The correct question is-"For a G.P the ratio of the 7th and 3rd term is 16. the sum of 9 terms is 2555. what is first term?"

Let us assume that, the first term of the geometric progression be b and let the common ratio be k.

Now the nth term of the progression is $bk^{n-1}$

Therefore the ratio of 7th term and 3rd term is $\frac{bk^{7-1}}{bk^{3-1}} =k^{4}$

Given that this ratio is 16.Hence we write,$k^{4}=16= > k=16^{\frac{1}{4}}=2$

Sum of n terms of a G.P is given by the relation

$\frac{b(k^{n}-1)}{k-1}$

Therefore,sum of 9 terms of the progression is $\frac{b(2^{9}-1)}{2-1} =511b$

Given that this sum is 2555 Hence we have $511b=2555= > b=5$

Therefore,The first term of the geometric progression is found to be 5

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