Question

for a G p a = 4/3 and t 7 = 243/1024 find the value of r​

Answer 1

Step-by-step explanation:

For a g.p. a=4/3 and t7=243/1024 find the value of r

Given:

$a=\frac{4}{3} \:$

$t_7=\frac{243}{1024}$

$using</p><p> \\ </p><p>\boxed{\text{n th term of G.P is }t_n=ar^{n-1}} \:$

$\implies\:ar^6=\frac{243}{1024} \:$

$</p><p>\implies\:(\frac{4}{3})r^6=\frac{243}{1024}</p><p> \:$

$\implies\:r^6=\frac{729}{4096} \:$

$\implies\:r^6=\frac{3^6}{4^6} \:$

$</p><p>\implies\:r^6=(\frac{3}{4})^6</p><p> \:$

$\implies\:\boxed{\bf\:r=\pm\frac{3}{4}} \:$

Answer 2

Answer:

The given values

a= 4/3

t7 = 243/1024

We need to find r

To find thr n th term in G.P we have a formula

tn = ar^n-1

Here n = 7

t7 = 4/3 × r^7-1

243/1024 = 4/3 × r^6

By simplifying we can get the value of r as

729/4096 = r^6

Taking square root on both sides, we get

27/64 = r^3

Taking cube root on both sides, we get

3/4 = r

r = 3/4

Hopes it helps

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