For the sequence $4, 8, 12, 16, . . .$ , find (i) general rule (ii) $n t h$ term (iii) $100 t h$ term.

Open in App

Solution

Step 1: General rule
In the sequence,
$1 s t$ term $4 = 4 \times 1$
$2 n d$ term $8 = 4 \times 2$
$3 r d$ term $12 = 4 \times 3$
$4 t h$ term $16 = 4 \times 4$
As these terms are multiples of $4$ .
So, the general rule is $' m u l t i p l e s o f 4'$ .
Step 2: $n t h$ term
$n t h$ term $= 4 \times n = 4 n$ (where $n$ is a natural number)
Step 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 $= 4 n$
$= 4 \times 100 = 400$
Therefore, General rule is $' m u l t i p l e s o f 4'$ , $n t h$ term $= 4 n$ and $100 t h$ term $= 400$ .

Suggest Corrections

Similar questions

Find the general term $(n^{t h} t e r m)$ and $23^{r d} t e r m$ of the sequence 3, 1, -1, -3, ......... .

23 \frac{1}{4,} 22 \frac{1}{2,} 21 \frac{3}{4}

(i) Which term of the sequence $24, 23 \frac{1}{4}, 22 \frac{1}{2}, 22 \frac{3}{4}, \dots \dots$ is the first negative term ?

(ii) Which term of the sequence $12 + 8 i, 11 + 6 i, 10 + 4 i, \dots \dots$ is (a) purely real (b) purely imaginary ?

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

Join BYJU'S Learning Program