Complete the recursive formula of the geometric sequence 7, - 14,28,-56

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

r=-2 an = 7 (-2) ^n-1

Step-by-step explanation:

According to my calculations