For the sequence $12, 24, 36, . . .$ , find (i) general rule (ii) $n t h$ term (iii) $100 t h$ term.

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Solution

(1): General rule
In the sequence,
$1 s t$ term $12 = 12 \times 1$
$2 n d$ term $24 = 12 \times 2$
$3 r d$ term $36 = 12 \times 3$
As these terms are multiples of $12$ .
So, the general rule is $' m u l t i p l e s o f 12'$ .
(2): $n t h$ term
$n t h$ term $= 12 \times n = 12 n$ (where $n$ is a natural number)
(3): $100 t h$ term
$100 t h$ term means $n = 100$
Substituting the value of $n$ in $n t h$ term.
$∴$ $100 t h$ term $= 12 n$ $= 12 \times 100 = 1200$
Therefore, General rule is $' m u l t i p l e s o f 12'$ , $n t h$ term $= 12 n$ and $100 t h$ term $= 1200$ .

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