Question

A sequence is defined recursively by the formula f(n + 1) = –2f(n). The first term of the sequence is –1.5. What is the next term in the sequence?

–3.5
–3
0.5
3

Answer 1

✏️ Development:

⭐ Initially, we have to find the reason why it was -1.5:

`\large {\text {$ \sf f (n+1) = -2 f(n) $}}`

➡️ Having n, then we'll find the value of n, then we'll replace it with the found result.

`\large {\text {$ \sf f (x+1) = -2.x = -1,5 $}}`

⌛ So, we will have to find what x is worth in this case:

`\large {\text {$ \sf f ( 0,75 +1 ) = -2 \cdot 0,75 $}}`

`\large {\text {$ \sf f ( 0,75) = -1,5 $}}`

→ Knowing this...

`\large {\text {$ \sf f ( 1,5 + 1 ) = -2 \cdot 1,5 $}}`

`\large {\boxed {\boxed {\sf f ( 2,5 ) = -3 }}}`
`\checkmark`

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Answer 2

The answer is 3

Explanation:

It's just wisdom I mean think about it it

1.5 then 3