Question

In a GP the first term is 7 the last term is 448 and the sum 889 find commmon ratio

Answer 1

Answer is in the above given attachment

Answer 2

The common ratio is 2.

Step-by-step explanation:

Given : In a GP the first term is 7 the last term is 448 and the sum 889.

To find : Common ratio ?

Solution :

The G.P series in in the form, $a,ar,ar^2,ar^3,...$

Where, first term is a=7

last term is l=448

The sum is $S_n=889$

The last term formula is

$l=ar^{n-1}$

$448=(7)r^{n-1}$

$r^{n-1}=\frac{448}{7}$

$r^{n-1}=64$

$r^{n-1}=2^6$

On comparing,

n-1=6 and r=2

n=7

The number of terms is 7.

The common ratio is 2.

For check,

The sum formula is  $S_n=\frac{a(r^n-1)}{r-1}$

$S_n=\frac{7(2^7-1)}{2-1}$

$S_n=\frac{7(128-1)}{1}$

$S_n=7(127)$

$S_n=889$

Therefore, the common ratio is 2.

#Learn more

The sum of first four terms of an gp is 30 and the sum of the first and the last term is 18 find the terms

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