Question

What are the next three terms of 1,-2,4

Answer 1

Next three terms are -8, 16 and -32

Explanation:

We are given the sequence:-

1, -2, 4, ...

We want to find next three terms:-

1, -2, 4, a4, a5, a6, ...

Since the sequence is geometric because it has common ratio;-

-2/1 = -2

4/-2 = -2

Our common ratio is -2.

General Term of Geometric

`\displaystyle \large{a_n = a_1 {r}^(n - 1) }`

Our first term or a1 is 1

Our common ratio or r is -2

Therefore:-

`\displaystyle \large{a_n =1 {( - 2)}^(n - 1) }`

Since we want to find next three terms which are a4,a5 and a6. Substitute n = 4,5 and 6 in.

Finding a4

`\displaystyle \large{a_4 = 1 {( - 2)}^(4 - 1) } \\ \displaystyle \large{a_4 = 1 {( - 2)}^(3 ) } \\ \displaystyle \large{a_4 = 1 {( - 8)} } \\ \displaystyle \large{a_4 = - 8}`

Finding a5

`\displaystyle \large{a_5 = 1 {( - 2)}^(5 - 1) } \\ \displaystyle \large{a_5 = 1 {( - 2)}^(4 ) } \\ \displaystyle \large{a_5= 1(16)}\\ \displaystyle \large{a_5 = 16}`

Finding a6

`\displaystyle \large{a_6= 1 {( - 2)}^(6- 1) } \\ \displaystyle \large{a_6 = 1 {( - 2)}^(5 ) } \\ \displaystyle \large{a_6 = 1( - 32)}\\ \displaystyle \large{a_6 = - 32}`