Data:
a5 = - 48
Being r = q = 2
a1 = ?
a8 = ?
n (Number of terms)
Solving:
Formula (geometric progression)
[tex]a_{n} = a_{1} *q^{n-1}[/tex]
We have:
find the 1th (a1)
[tex]a_{n} = a_{1} *q^{n-1}[/tex]
[tex]a_{5} = a_{1} *2^{5-1}[/tex]
[tex]-48 = a_{1} *2^{4}[/tex]
[tex]-48 = a_{1} *16[/tex]
[tex] 16a_{1} = -48[/tex]
[tex] a_{1} = \frac{-48}{16} [/tex]
[tex] \boxed{a_{1} =-3}[/tex]
find the 8th (a8)
[tex]a_{n} = a_{1} *q^{n-1}[/tex]
[tex]a_{8} = -3 *2^{8-1}[/tex]
[tex]a_{8}= -3 *2^{7}[/tex]
[tex]a_{8}= -3 *128[/tex]
[tex] \boxed{a_{8} =-384}[/tex]
Answer:
[tex] \boxed{a_{1} = -3}[/tex]
[tex] \boxed{a_{8} = -384}[/tex]
