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

Answer:

False

Step-by-step 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