Question

How many terms of G.P. 4,2,1.... Amount to 127/16

Answer 1

Answer:

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Answer 2

There are approximately 7 terms.

Step-by-step explanation:

Since we have given that 4,2,1.....................

Amount to $\dfrac{127}{16}$

Here, a = 4 ( first term)

r = $\dfrac{a_2}{a_1}=\dfrac{2}{4}=0.5$ (common difference)

So, the sum of n terms in GP would be

$S_n=\dfrac{a(1-r^n)}{1-r}\\\\\dfrac{127}{16}=\dfrac{4(1-0.5^n)}{1-0.5}\\\\\dfrac{127}{16}=\dfrac{4-4\times 0.5^n}{0.5}\\\\\dfrac{127}{16}\times 0.5=4-4\times 0.5^n\\\\3.96=4-4\times 0.5^n\\\\3.96-4=-4\times 0.5^n\\\\\dfrac{0.03125}{4}=0.5^n\\\\0.0078125=0.5^n\\\\n=7$

Hence, there are approximately 7 terms.

# learn more:

1 + 2 + 4 + 8 + 16 +....

127,

3. How many terms of G.P. 4, 2, 1..... amount to

in 108 Find the

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