- #1

misogynisticfeminist

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In a geometric progession, the first term is 12 and the fourth term is -3/2. Find the sum to n terms and the sum to infinity. Find also, the least value of n for which the magnitude of the difference between the sum to infinity and to n terms are less than 0.001.

I have first expressed the GP as,

[tex] 12, T_2, T_3, -3/2 [/tex]

I see that the ratio between the 4th and 1st terms is [tex] -\frac{1}{8} [/tex] and this is 3 times the common ration r, which is -1/24. To find the sum to n terms, i get,

[tex] S_n =\frac {12 ( - \frac {1}{24} ^n -1 )}{-1/24-1} [/tex]

and the sum to infinity is 11.52. However the sum to infinity is given as 8 in the answer.

To find the last part of the question, i did,

[tex] 11.52- \frac {12 ( - \frac {1}{24} ^n -1 )}{-1/24-1} = 0.001 [/tex] but it didn't work out to get the answer or n=13.

Thanks a lot for your help.