How do you find S_nSn for the geometric series a_1=343a1=343, a_n=-1an=−1, r=-1/7?

1 Answer
Binayaka C. · Jumbotron
Jul 10, 2017

S_n = 300Sn=300

Explanation:

a_1=343 , a_n= = -1 , r= -1/7a1=343,an==−1,r=−17

Given that

a_n = "last term"an=last term

a_1 = "first term"a1=first term

r = -1/7r=−17

T_n = a_1 cdot r^(n-1)Tn=a1⋅rn−1

Recall that T_n = a_nTn=an

Hence ->→ a_n = a_1 cdot r^(n-1)an=a1⋅rn−1

a_n= a_1*r^(n-1) or 343 * (-1/7)^(n-1) = -1 or (-1/7)^(n-1) = -1/343 an=a1⋅rn−1or343⋅(−17)n−1=−1or(−17)n−1=−1343 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]

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