Find the next three terms of the following sequence. 8, 24, 72, … - Vidyadip

Question

Find the next three terms of the following sequence.
$8, 24, 72, …$

✓

Answer

$8, 24, 72, …$
In an arithmetic sequence $a = 8,$
$d = t2 – t1 = t3 – t2$
$= 24 – 8 = 72 – 24$
$= 16 \neq 48$
So,it is not an arithmetic sequence. In a geometric sequence,
$r=\frac{t_2}{t_1}=\frac{t_3}{t_2}$
$\Rightarrow \frac{24}{8}=\frac{72}{24}$
$\Rightarrow 3=3$
$\therefore$ It is a geometric sequence
$\therefore$ The $n ^{\text {th }}$ term of a G.P is $t_n=\operatorname{ar}^{n-1}$
$\therefore t _4=8 \times 3^{4-1}$
$=8 \times 3^3$
$=8 \times 27$
$=216$
$t _5=8 \times 3^{5-1}$
$=8 \times 3^4$
$=8 \times 8$
$=648$
$t_6=8 \times 3^{6-1}$
$=8 \times 3^5$
$=8 \times 243$
$=1944$
The next 3 terms are $8,24,72,216,648,1944$.

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