Question

Consider the following sequence

Answer 1

Answer:

Solution given:

first term [a]=152

second term[b]=-76

common ratio[r]=$\frac{-76}{152}$=-1/2

now

for nth term ,we have

nth term =a ${r}^{n -1}$

now

7th term==152${-1/2}^{7 - 1}$

=152×1/64=19/8

Answer 2

Answer:

a₇ =  2.375

Step-by-step explanation:

There is a common ratio r between consecutive terms, that is

r = $\frac{-76}{152}$ = $\frac{38}{-76}$ = $\frac{-19}{38}$ = - $\frac{1}{2}$

This indicates the sequence is geometric with nth term

$a_{n}$ = a₁ $(r)^{n-1}$

where a₁ is the first term and r the common ratio

Here a₁ = 152 and r = - $\frac{1}{2}$ , then

$a_{n}$ = 152 $(-\frac{1}{2}) ^{n-1}$ , so

a₇ = 152 $(-\frac{1}{2}) ^{6}$ = 152 × $\frac{1}{64}$ = 2.375