Question

Each term of a certain sequence is greater than the term before it. The difference between any two consecutive terms in the sequence is always the same number. If the fourth and the ninth term of the sequence are 121 and 176 respectively, what is the value of the second term?

Answer 1

thxs for helping me mebs. ;__; means so much. i really want to improve my SAT score D':

Answer 2

a1 a2 a3... its an arithmatic sequence so.... recall that \[an = a1 + (n-1)d\]

you know that that 121 = a4 + (4-1)d

you also know that 176 = a9 +(9-1)d

Answer 3

and a4 and a9 are the same term...

Answer 4

so know we can say that :

176 - 8d = 121 - 3d right? you follow?

Answer 5

wait how are they the same D:

Answer 6

because the first term is the same...

Answer 7

remember that the same sequence has the same first term... right.. please tell you studied geometric and arithmetic sequences.... you did right?

Answer 8

yes, but i forgot it :(

Answer 9

that's ok lets review....

here is a sequence: 2 , 4 , 6 , 8 , 10

here is another sequence: 2 , 4, 8, 16, 32

what is it and what Is the difference.

Answer 10

First sequence: arithmetic, d = 2
2: geometric, r = 2

Answer 11

good good... now for this one we are doing

the general formula an = a1 + (n-1)d then a1 is the first term for the arithmetic sequence... so that's why I said a4 and a9 are the same...

Answer 12

when you said,

"you know that that 121 = a4 + (4-1)d

you also know that 176 = a9 +(9-1)d"
does it work if i do this to it
121 = 121 + (4-1)d
176 = 176 + (9-1)d ?

Answer 13

no that's not right 121 is the 4th term not the 1st tem... and 176 is the 9th term not the 1st term...

Answer 14

its
121 = a1 +(3)d
176 = a1 +(8)d

Answer 15

ohhhhh oh oh ohhhh xD omg, i see it. thx thx :D sorry for my brain. xD

Answer 16

good nor rearrange for a1 and now you get

a1 = 121 -3d
a1 = 176 -8d

alright?

Answer 17

yes :)!

Answer 18

now you can solve this simple equation of

176 - 8d = 121 -3d right? whats the answer?

Answer 19

d is 11 :D!~~~

Answer 20

good now find what a is

Answer 21

then add 11 to it to find the second term and your done!

Answer 22

BD
Thanks again
a2 = 99

Answer 23

well done! yw