Question

From the following table, find $a+b+c+d+e+f+g+h+i+j$

$8$	$16$	$32$	a
$1$	$5$	b	$125$
$10$	$30$	$90$	c
$1$	$7$	d	$343$
$72$	$36$	$18$	e
$216$	$72$	f	$8$
$750$	g	$30$	$6$
$686$	h	$14$	$2$
$10,000$	$1000$	i	$10$
$648$	$108$	j	$3$

Answer 1

Let's understand the relationship between the numbers in each row.

Row 1: The numbers are 8, 16, 32, a

Each subsequent term is 2 times the preceding term.

16 = 2 x 8

32 = 2 x 16

Hence, a = 2 x 32 = 64

Row 2: The numbers are 1, 5, b, 125

5 = 1 x 5 = last term x 5

Let's see if we put b = Last erm x 5 = 5 x 5 = 25, is the sequence still obeyed. If b = 25 then next term in the sequence should be 5 x b = 5 x 25 = 125, which indeed is the case. Hence, b = 25

Row 3: 10, 30, 90, c

30 = 3 x 10

90 = 3 x 30

Hence, the sequence is 3 times the preceding term.

Hence, c = 3 x 90 = 270

Row 4: 1, 7, d, 343

7 = 7 x 1 i.e 7 times the preceding term. Let's say this is obeyed by "d" also.

Hence, d = 7 x 7 = 49

And the next term by this logic should be 7 x 49 = 343, which indeed is the case. Hence d = 49

Row 5: 72, 36, 18, e

36 = 0.5 x 72

18 = 0.5 x 18

Every subsequent term is half of the preceding term. Hence, e = 0.5 x 18 = 9

Row 6: 216, 72. f, 8

72 = one third of 216

Maintaining the trend, f = one third of 72 = 24

if this is correct then next term should be one third of 24 = 8, which indeed is the case. Hence, f = 24.

Row 7: 750, g, 30, 6

30 = 5 x 6, the preceding term is 5 times the subsequent term.

By this logic, g = 5 x 30 = 150

and term preceding g should be 5 x g = 5 x 150 = 750, which actually is the case. Hence, g = 150.

Row 8: 686, h, 14, 2

By now you would have understood the logic. The preceding term is 7 times the subsequent term. Hence, h = 7 x 14 = 98

Row 9:

Every subsequent term is one tenth of the previous term. hence, i = 1/10 x 1000 = 100

Row 10:

Every subsequent term is one tenth of the previous term. hence, j = 1/6 x 108 = 18

Hence, a +b+c+d+e+f+g+h+i+j = 64+25+270+49+9+24+150+98+100+18= 807