Find the indicated sum 5 1 3 7 4 middot 12 9 a 408 b 49

Find the indicated sum. -5 -1 + 3 + 7 +... + [4 middot 12 - 9] (a) 408 (b) 492 (c) 204 (d) 246 1/4 + 1/2 + 1 + 2 + 4... + 1/4 middot 2^10-1 (a) 195.75 (b) 255.75 (c) 641.25 (d) 1281.25 48 + 12 + 3 + 3/4 + 3/16.... (a) 120.5 (b) 648.25 (c) 64 (d) 196

Solution

14) 1/4 + 1/2 + 1 +2 +4....(1/4)2^10-1

G.P with common ratio = 2 ; a1 = 1/4

an = (1/4)(2)^n-1 = (1/4)2^10 -1 ;

n = 10

So, sum of G.P. a1(1- r^n)/(1- r ) = (1/4)[1 - 2^10]/(1-2)

= (2^10 -1)/4

= 255.75 Option b