Question

17. Find the next number in the following
number series.
24, 48, 52, 156, 162,
(1) 546
(2) 1168
(3) 648
(4) 638​

Answer 1

$Given \: series \: 24,48,52,156,162,?$

/* Observe the sequence, we can find following pattern */

$1) First \:term (a_{1}) = 24$

$2) Second \: term (a_{2})\\= 2\times a_{1} \\= 2 \times 24 \\= 48$

$3) Third \: term (a_{3}) \\= = a_{2} + 4\\= 48 + 4 \\= 52$

$4) Fourth \: term (a_{4})\\= 3\times a_{3} \\= 3 \times 52 \\= 156$

$5) Fifth \: term (a_{5}) \\= = a_{4} + 6\\= 156+ 6 \\= 162$

$\red{ 6) Sixth \: term (a_{6})}\\= 4\times a_{5} \\= 4 \times 162 \\\green {= 648 }$

Therefore.,

$\red{ Required \:next \:number }\green { = 648}$

$Option \: \green { ( 3 ) } \: is \: correct .$

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