Question

A sequence of numbers follows the rule: multiply the previous number by -2 and add 3. The fourth term in the sequence is -7. Give the next 3 terms in the sequence. Give the 3 terms that came before -7 in the sequence.

Answer 1

Next 3 terms: 17, -31, 65

3 terms before -7: 2, -1, 5

Explanation:

Fourth term in the sequence = -7

Rule for finding the next term:

`a_n=-2* a_(n-1)+3`

Therefore, the fifth term:

`a_5=-2* a_4+3\\\Rightarrow a_5=-2* -7+3\\\Rightarrow \bold{a_5=17}`

Sixth term:

`a_6=-2* a_5+3\\\Rightarrow a_6=-2* 17+3\\\Rightarrow \bold{a_6=-31}`

Seventh term:

`a_7=-2* a_6+3\\\Rightarrow a_7=-2* -31+3\\\Rightarrow \bold{a_7=65}`

Let the three terms that came before -7 be:
`x, y, z`

As per question statement:

`a_n=-2* a_(n-1)+3`

`-7 = -2* z+3\\\Rightarrow -2z=-10\\\Rightarrow z=5`

Again applying the given rule:

`5 = -2* y+3\\\Rightarrow y =-1`

Again applying the given rule:

`-1 = -2* x+3\\\Rightarrow x =2`

Therefore the 3 terms before -7 are:

2, -1, 5