Answer:
tₙ = -2tₙ₋₁
Step-by-step explanation:
Recursive formulas for geometric sequences are written tₙ = r(tₙ₋₁)
"tₙ" means the "nth term", the term value you are finding
"tₙ₋₁" means the "term before the nth term", or the previous term
"r" means the common ratio
First, we need to find the common ratio, which is by what number the previous term multiplies by to get the next term.
To find this number, divide one of the values by the previous value.
t₃ ÷ t₂ Substitute the values of term 3 and term 2
= 28 ÷ -14 Divide
= -2 Common ratio
tₙ = r(tₙ₋₁) Substitute the common ratio into the formula
tₙ = -2tₙ₋₁
Example:
If you wanted to get the term after -56, you would logically multiply -56 by 2. Using the formula:
tₙ = -2tₙ₋₁
t₅ = -2t₅₋₁ The term after -56 will be the 5th term
t₅ = -2t₄ The term before term 5 is term 4
t₅ = -2(-56) Substitute the value of term 4
t₅ = 112
