Question

Question 15 Given a G.P. with a = 729 and 7th term 64, determine S7.

Class X1 - Maths -Sequences and Series Page 192

Answer 1

$Given,a=729\\and,T_7=64\\\\\\T_n=ar^{n-1}\\T_7=ar^{7-1}=64\\729r^6=64\\r^6=\frac{64}{729}\\\\r^6=(\frac{2}{3})^6\\\\r=\frac{2}{3}$
now, use formula,
$s_n=\frac{a(1-r^n)}{1-r}, when,r\leq1\\\\S_7=\frac{729[1-(\frac{2}{3})^7]}{1-\frac{2}{3}}\\\\=\frac{729[1-\frac{128}{2187}]}{\frac{1}{3}}\\\\=\frac{729.3}{1}.\frac{2187-128}{2187}\\=2059$

Answer 2

Given that

a = 729
T7 =64

We know that

Tn = ar^n-1
T7 =729r^7-1=64

729r^6 = 64

r^6 = 64/729

r^6 =(2/3)^6

r = 2/3

we know that

Sn = a ( 1 - r^n)/(1 - r)

Sn = 729 ( 1 - 2/3^6 )/(1 - 2/3)

Sn = 729 ( 1 - 128/2187)/1/3

Sn = 729.3/1 ( 2187 -128/2187)

Sn = 2059