Geometric Sequence problem

Question

For a geometric sequence, term 4 = 4x + 8 and term 7 = x – 4. If the common ratio is 1/2, what is the first term?

Answer 1

terms 1,2,.. in the geometric sequence

correspond to f(x)=Ab⁰,Ab¹,... for exponential function

have then

4x+8=A(1/2)³,,,,given b=1/2 for fourth term

x-4=A(1/2)⁶ ,,, for seventh term

[4x+8]/[x-4]=(1/2)^-3=8

x=10

48=A(1/2)³

A=384

Answer 2

first term = 384

384, 192, 96, 48, 24, 12, 6 are the 1st 7 terms

a1, a2, a3, a4, a5, a6, a7

4th term = 48

7th term = 6

r=1/2

an = a1(r^(n-1))

a4 = a1(1/2)^3 = a1/8 = 384/8 = 48

a7 = a1(1/2)^6 = a1/64 = 384/64 = 6

a4 = 4x+8 = 4(10) +8 = 6, x=10

a7 = x-4 = 10-4 = 6

x=10