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find the value of n if the sum of n terms of the series 11 + 33 + 99 + ... is equal to 108 251.
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This progression is geometric with the first term 11 and the common ratio of 3.
Use the formula for the sum of the first n terms of a geometric progression:
= .
(see the lesson Geometric progressions in this site).
Substitute here a = 11 and q = 3. You will get an equation
= , or
= = 9841,
= 2*9841 + 1 = 19683 = 3^9.
Hence, n = 9.
Answer. n = 9.
