$a_8=6561$

Hallo all,

since it is a geometric,as refers to a(number of term),

given that a(4) = 81, a(8) = 6561,

a(4) = ar^3 = 81 , a(8) = ar^7 = 6561,

a = 81 / r^3(1)

ar^7 = 6561(2)

substitute (1) into (2),

81 / r^3 x (ar^7) = 6561

81r^4= 6561

r^4 = 81(since the initial term is negative),

r^4 = (-3)^4

r = -3

so the initail term that is a = 81 / (-3)^3 = 81 /-27 = -3,

therefore sum of the 1st 4 terms(noted that r=-3),

use S(n) = a(1 - r^n) / 1-r

S(4) = -3 ( 1-(-3)^4) / 1-(-3)

S(4) = -3 ( 1 -81) / 1 + 3

S(4) = -3(-80) / 4 = 240 /4 = 60, therefore S(4) = 60....

thanks....

make the first term as Q,, and term 1 as X1 term 2 as x2 and continous

x4 = Q R^n-1 N = line of term 81 = Q R^3 because N =4 (term 4) Q = 81/R^3 ............................ (1)

X8 = Q R^n-1 6561 = Q R^7 Q = 6561/R^7 ........................ (II)

so, join the 1 and 2 81/R^3 = 6561/R^7 R^4 = 81 R = plus minus 3

Q = 81/27 = -3 because negative initial form, we till take R as minus 3 so line up -3 , 9, -27, 81 sum of 4 first term = 60 you can use formula, but since this problem not so hard, i just calculated them on my own,,