Question

The 80th term of an arithmetic sequence is twice the 30th term. If the first term is 7, what is the 40th term?

Answer 1

what do you know about arithmetic sequence so far?

Answer 2

what do you mean?

Answer 3

if you have treated arithmetic sequence, what are the formulas relating to an arithmetic sequence do you know?

Answer 4

idk. we've learned about finding rules from a sequence before. does that make sense?

Answer 5

do you know the following formula?
\[\Large a_n =a_1+(n-1)d\]
fro finding the nth term of an arithmetic sequence?

Answer 6

no

Answer 7

then you would have difficulties understanding my explanation...

Answer 8

could you try to explain it to me?

Answer 9

okay.. i would try to explain...
since the 80th term is twice the 30th term,
\[\Large a_{80}=2a_{30}\]

Answer 10

so what does the d in the equation represent?

Answer 11

i would break that down a bit using the formula i gave above...
\[\Large a_1+(80-1)d=2(a_1+(30-1)d)\]
you were told in the question that the first term of the sequence which is a(1) is 7...
so
\[\Large 7+79d=2(7+29d)\]
\[\Large 7+29d=14+58d\]
from there, what do you get when you solve for d??

Answer 12

d represents the common difference between consecutive terms in the sequence.

Answer 13

why did you subtract 1 from 30 and 80?

Answer 14

that is what is in the formula..

Answer 15

i posted the formula above..

Answer 16

i got d=1/3

Answer 17

i made a mistake!
it is supposed to be
\[\Large 7+79d=14+58d\]

Answer 18

that's what i got and i solved for d.

Answer 19

can you please post your working?

Answer 20

7+(80-1)d=2(7+(30-1)d)
7+79d=2(7+29d)
7+79d=14+58d
21d=7
d=1/3

Answer 21

yh..you are right!
i made a mistake!

Answer 22

okay now that you have found d from the information given in the question,
you can now find the 40th term using the same formula i posted above..
\[\Large a_{40}=7+(40-1)\times \frac{ 1 }{ 3 }\]

Answer 23

a(40) simply represents the 40th term