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

Answer:

Next 3 terms: 17, -31, 65

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

Step-by-step explanation:

Fourth term in the sequence = -7

Rule for finding the next term:

$a_n=-2\times a_{n-1}+3$

Therefore, the fifth term:

$a_5=-2\times a_4+3\\\Rightarrow a_5=-2\times -7+3\\\Rightarrow \bold{a_5=17}$

Sixth term:

$a_6=-2\times a_5+3\\\Rightarrow a_6=-2\times 17+3\\\Rightarrow \bold{a_6=-31}$

Seventh term:

$a_7=-2\times a_6+3\\\Rightarrow a_7=-2\times -31+3\\\Rightarrow \bold{a_7=65}$

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

As per question statement:

$a_n=-2\times a_{n-1}+3$

$-7 = -2\times z+3\\\Rightarrow -2z=-10\\\Rightarrow z=5$

Again applying the given rule:

$5 = -2\times y+3\\\Rightarrow y =-1$

Again applying the given rule:

$-1 = -2\times x+3\\\Rightarrow x =2$

Therefore the 3 terms before -7 are:

2, -1, 5