SOLUTION: find the value of n if the sum of n terms of the series 11 + 33 + 99 + ... is equal to 108 251.

Question 1012940: find the value of n if the sum of n terms of the series 11 + 33 + 99 + ... is equal to 108 251.
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.
find the value of n if the sum of n terms of the series 11 + 33 + 99 + ... is equal to 108 251.
----------------------------------------------------------------------

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.

RELATED QUESTIONS
if the sum of first n terms of the series 5,9,13,17,....is 275 then find n. (answered by josgarithmetic)

The sum of n term of a series is n^2+2n for all value of n.find the first three terms of... (answered by mccravyedwin)

Find the general formula for the sum of this series: 3+33+333+3333+... to n terms (answered by Edwin McCravy)

If there are (2n+1) terms in an arithmetic series, prove that the ratio of the sum of odd (answered by richard1234)

Can someone please help me? 1. Find the sum of each arithmetic series. Part I: -15 + -3 (answered by josgarithmetic)

Find the 10th term of a series in Arithmetic series, whose sum to n terms is 3n+4n2(4 n... (answered by solver91311)

Find the sum to n terms of the... (answered by 1136877,meng)

The sum of the first n terms of a series is 2n^2−n. Find the nth... (answered by ikleyn)

the sum of the first n terms of a series is 2n^-n find the nth... (answered by Edwin McCravy)