How do you find $S_n$ for the geometric series $a_1=343$ , $a_n=-1$ , r=-1/7?

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Answer 1 · 2017-07-10T12:34:24

$S_n = 300$

$a_1=343 , a_n= = -1 , r= -1/7$

Given that

$a_n = "last term"$

$a_1 = "first term"$

$r = -1/7$

$T_n = a_1 cdot r^(n-1)$

Recall that $T_n = a_n$

Hence $->$ $a_n = a_1 cdot r^(n-1)$

$a_n= a_1*r^(n-1) or 343 * (-1/7)^(n-1) = -1 or (-1/7)^(n-1) = -1/343$ or

$(-1/7)^(n-1) = (-1/7)^3 :. n-1 = 3 or n =4$

$S_n = a_1 * ( r^n -1)/(r-1) = 343 * ((-1/7)^4-1 ) /(-1/7-1)$

$=343*(1/2401-1)/(-8/7) = 343 * (-2400/2401)* (-7/8)$

$= cancel343* 300/cancel343 =300$

$S_n = 300$ [Ans]

How do you find S_nS_n for the geometric series a_1=343a_1=343, a_n=-1a_n=-1, r=-1/7?