Answer:
a₇ = 2.375
Step-by-step explanation:
There is a common ratio r between consecutive terms, that is
r = [tex]\frac{-76}{152}[/tex] = [tex]\frac{38}{-76}[/tex] = [tex]\frac{-19}{38}[/tex] = - [tex]\frac{1}{2}[/tex]
This indicates the sequence is geometric with nth term
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 152 and r = - [tex]\frac{1}{2}[/tex] , then
[tex]a_{n}[/tex] = 152 [tex](-\frac{1}{2}) ^{n-1}[/tex] , so
a₇ = 152 [tex](-\frac{1}{2}) ^{6}[/tex] = 152 × [tex]\frac{1}{64}[/tex] = 2.375
Answer:
Solution given:
first term [a]=152
second term[b]=-76
common ratio[r]=[tex] \frac{-76}{152}[/tex]=-1/2
now
for nth term ,we have
nth term =a [tex] {r}^{n -1} [/tex]
now
7th term==152[tex] {-1/2}^{7 - 1} [/tex]
=152×1/64=19/8
