the 3rd term of a g.p is 63 while the 5th term is 567,what is the sum of the first 7 terms
t(5) = ar^4 = 567
t(3) = ar^2 = 63
divide first equation by the second
ar^4/(ar^2) = 567/63
r^2 = 9
r = ± 3
if r = ±3,
ar^2= 63
a = 7
Since you only want 7 terms, it would probably be faster to just find them and add them up
that is,
7 + 21 + 63 + 189 + 567 + 1701 + 5103 = 7651
or 7 - 21 + 63 - 189 + 567 - 1701 - 5103 = ......
or by formula
if a=7, r= 3
sum(7) = 7(3^7 - 1)/(3-1) = 7651
or if x=-3
sum(7) = 7((-3)^7 - 1)/(-3-1) = .....
The third term of a g p is 63 while the 5th term is 567 what is the sum of the first seven terms
THE SECOND AND FOURTH TERMs OF A GP ARE 8 AND 32 RESPECTIVELY .FIND THE SUM OF THE FIRST NINE TERMs.
t(4) = ar³ = 32... (1)
t(2) = ar = 8... (2)
Find; S9
t(4)/t(2) = ar³/ar = 32/8
r² = 4
r = 2.
if r = ±2,
ar³= 32
a = 4
Therefore;
r = 2
t(1) = a = 4
t(2) = a.r = 4 × 2 = 8
t(3) = a.r² = 8 × 2 = 16
t(4) = a.r³ = 16 × 2 = 32
t(5) = a.r⁴ = 32 × 2 = 64
t(6) = a.r⁵ = 64 × 2 = 128
t(7) = a.r⁶ = 128 × 2 = 256
t(8) = a.r⁷ = 256 × 2 = 512
t(9) = a.r⁸ = 512 × 2 = 1024
S9 = 4+8+16+32+64+128+256+512+1024 = 2044