Number Sequence

Question

please show solution

3/7 8/4 5/9 7/11 12/18 ______

Answer key shows 9/13 is the next. Choices are 9/13, 15/11, 14/10, 12/9, and 11/15.

30 42 74 126 198 _______

Answer key shows 2810, but I think the answer is 290 which is not on the choices. Choices are 219, 279, 2810, 3110, and 3114.

Answer 1

For the 2nd sequence let find more complicated pattern to get one of choices. Separate each number for 2 parts:

3|0 4|2 7|4 12|6 19|8

Left parts: 3 4 7 12 19. Next number should be 28

Right parts: 0 2 4 6 8. Next number should be 10

So the next term is 28|10, or 2810

Answer 2

3/7, 8/14, 5/9, 7/11, 12/18, 9/13 are in increasing order (assuming 8/14, not 8/4)

3/7<8/14<5/9<7/11<12/18<9/13

the sequence starts at a little less than 1/2 and ends with a little more than 2/3

in rounded decimal form the terms are

.43, .57, .56, .64, .67, .69 11/15 = .73 14/10 = 1.40, 12/9 = 1.33, 15/11 = 1.36

9/13 seems to fit the smaller increase in the sequence. 11/15 is 2nd best answer

but maybe someone else sees another pattern

30, 42, 74, 126, 198, 2810, 3912,

break it into two parts 3-0, the 3 increases by consecutive odd numbers: 3, 4, 7, 12, 19, 28

3+1 =4, 4+3+ 7, 7+5 = 12, 12+7 = 19, 19+ 9= 28, 28+11 = 39, 39+13 = 52

the 2nd part increases by 2 each term: 0+2=2, 2+2=4, 4+2+ 6, 6+2 = 8, 8+2=10, 10+2 = 12, 12+2=14

Now put the two parts together: 30, 42, 74, 126, 198, 2810, 3912, 5214

I can see how you might think 290 though. put 280 with 10 and if the 1 and 8 overlapped, you'd get 290

Answer 3

It looks like your practice book is garbage, or you are not writing the right sequences. Generally, the sequences on the SAT are arithmetic or geometric. You could make a case for the 2nd sequence to be following the rule a₁ = 30 a_n = (2n-1)*10 + 2(n-1) , in which case 290 would be the correct a₆. The first "sequence" is not a sequence. and the second sequence is unlikely on the SAT, but you have the right idea: look at differences and quotients between terms and look for patterns.