Question

. Find the sum of the geometric sequence. (1 point) 1, one divided by four, one divided by sixteen, one divided by sixty four, one divided by two hundred and fifty six

Answer 1

341/256

Explanation:

I took the test and got the answer right

You just give all the fractions a common denominator of 256 and then change and add up the numerators and you get 341

Answer 2

0.332

Explanation:

given series

1/4, 1/16,1/64.1/256

this is geometric series

where common ratio r is given by

nth term/ (n-1)th term

let the second term is nth term and first term is (n-1)th term

r = 1/16 / (1/4) = 1/4

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sum of series is given by

a (1-r^n)/1-r

where a is first term

n is the number of terms

r is the common ration

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in the given series

1/4, 1/16,1/64.1/256

a = 1/4

r = 1/4

n = 4

thus ,

sum = 1/4(1-(1/4)^4)/ (1-1/4)

sum = 1/4(1-(1/256)/(4-1)/4

sum = 1/4((256-1)/256 / 3/4

1/4 in numerator and denominator gets cancelled

sum =( 255/256*3) = 255/768 = 0.332

Thus, sum of series is 0.332.