Question

For the following geometric sequence, find the recursive formula. {-80, 20, -5, ...}

Answer 1

Answer:

Step-by-step explanation:

first term,a=-80

common ratio,r=20÷-80

r=1/-4

general term of the sequence=a×r^n-1

=-80×(-1/4)^n-1

Answer 2

The recursive formula for the GP is $t_n = (-80){(\frac{-1}{4})}^{n-1}$.

• For the given geometric sequence we have to find the recursive formula or general term for the sequence.
• The general term for the GP is given by

$t_n = ar^{n-1}$

where $t_n$ is the $n^{th}$ term and a is the first term and r is the common ratio.

• Now, the given series is -80 , 20 ,-5 , ....

First term (a) = -80

Common ratio(r) = 20/-80 = -1/4.

• Now the recursive formula becomes -

Substituting the values in the expression of $n^{th}$ term.

$t_n = (-80){(\frac{-1}{4})}^{n-1}$