Question

Learning Task No.2

A. Find the missing terms and write the rules.
1. 5,6,8,15
2. 18,20,24_38
3. 14, 17, 20,23,
4. 24, 30, 36, 42,
5. 1, 10, 100,​

Answer 1

See Explanation

Explanation:

Required

Complete the term and identify the rule

`(a)\ 5, 6, 8, [], 15`

We have:

`5 + 1 = 6`

`6 + 2 = 8`

`8 + 3 = 11` --- Missing term

`11 + 4 = 15`

The rule is:

Add current term to the position of term

i.e.

`T_(n+1) = T_n + n`

`(b)\ 18, 20, 24, [], 38`

We have:

`18 + 2*1 = 20`

`20 + 2*2 = 24`

`24 + 2 * 3 = 30` --- Missing term

`30 + 2 * 4 = 38`

The rule is:

Add current term to twice the position of term

i.e.

`T_(n+1) = T_n + 2 *n`

`(3)\ 14, 17, 20, 23, []`

We have:

`14 + 3 = 17`

`17 + 3 =20`

`20 + 3 = 23`

`23 + 3 = 26` --- Missing term

The rule is: Add 3

i.e.

`T_(n+1) = T_n + 3`

`(4)\ 24, 30, 36, 42, []`

We have:

`24 + 6 = 30`

`30 + 6 = 36`

`36 + 6 = 42`

`42 + 6 = 48` --- Missing term

The rule is: Add 6

i.e.

`T_(n+1) = T_n + 6`

`(5)\ 1, 10, 100`

We have:

`10^0 = 1`

`10^1 = 10`

`10^2 = 100`

`10^3 = 1000` -- Missing term

The rule is: 10 to the power of current position

i.e.
`T_n = 10^n`