Question

Which of the following form a sequence?
(i) $4,11,18,25,........$ (ii) $43,32,21,10,........$
(iii) $27,19,40,70,........$ (iv) $7,21,63,189,...........$

Answer 1

(i) $4,11,18,25,.......$

$4+7=11,11+7=18,18+7=25$

Here, the difference between two consecutive numbers is fixed and are in increasing order.

Thus, form a sequence.

(ii) $43,32,21,10,........$

$43-32=11,32-21=11,21-10=11$

Here, the difference between two consecutive numbers is $11$. So, the next term is obtained by subtracting $11$ from previous number.

Thus, the numbers follow a pattern in decreasing order and form a sequence.

(iii) $27,19,40,70$

$27-19=8,19-40=-21,40-70=30$

The numbers does not differ by a fixed value and they don't follow any specific pattern.

Hence, it does not form a sequence.

(iv) $7,21,63,189$

$7\times 3=21,21\times 3=63,63\times 3=189$

So, they follow a pattern in which the next number is obtained by multiplying previous number by $3$.

Thus, they form a sequence.

Hence, (i), (ii) and (iv) form a sequence.