Question

STD 10

Mathematics

Lesson 5

Arithmetic progress

State whether true or false.

1) 6 , 12 , 18 , 24 , .......... , 284 is an A.P. ?​

ANSWER IS TRUE

Answer 1

False

Explanation:

Given

`6 , 12 , 18 , 24 , .......... , 284`

Required

Determine if it is an AP or not

First, calculate the common difference (d)

`d = 24 - 18=6`

`d = 18 - 12=6`

`d = 12 - 6=6`

Next, is to determine if the last term is valid using:

`T_n = a + (n - 1) d`

So, we have:

`284 = 6 + (n - 1) * 6`

`284 = 6 + 6n - 6`

Collect like terms

`284 = 6 - 6+ 6n`

`284 = 6n`

Divide by 6

`284/6 = n`

`n = 284/6`

`n = 47.33`

The value of n must be a positive whole number. Hence, it is not an AP