Plz expain how to solve dis : 23 If S1={2}, S2={3,6}, S3={4,8,16}, S4={5,10,20,40}, - Maths - Principle of Mathematical Induction

Question

Plz expain how to solve dis :

23 If S1={2}, S2={3,6},
S3={4,8,16}, S4={5,10,20,40}, then the sum of
numbers in the set S15 is

1) 5(215) 2) 16(215-1)

3) 16 (216-1) 4) 15(515-1)

Brijendra Pal · Accepted Answer

Hi, next number in a set is double of previousHere observe the first series S1 starts with 2 and has 1 term and S2 with 3 and has two term and S3 with 4 and has 3 term so obviously S15 will start with 16 and has 15 terms so sum of  S15 =16+32+64+
15 termsit is a GP with a = 16 and r = 2Sum =arn-1r-1= 16×215-12-1= 16×215-1

Plz expain how to solve dis...: 23. If S1={2}, S2={3,6}, S3={4,8,16}, S4={5,10,20,40},..... then the sum of numbers in the set S15 is . 1) 5(215) 2) 16(215-1) 3) 16 (216-1) 4) 15(515-1)

Plz expain how to solve dis...:

23. If S₁={2}, S₂={3,6}, S₃={4,8,16}, S₄={5,10,20,40},..... then the sum of numbers in the set S₁₅ is .

1) 5(2¹⁵) 2) 16(2¹⁵-1)

3) 16 (2¹⁶-1) 4) 15(5¹⁵-1)