Use the explicit formula an = a1 + (n - 1) * d to find the 1000th term of the sequence below.

24, 31, 38, 45, 52, ...

A. 7024
B. 7017
C. 6993
D. 7045
Would it be B?

Question

Use the explicit formula an = a1 + (n - 1) * d to find the 1000th term of the sequence below.

24, 31, 38, 45, 52, ...

A.	7024
 		B.	7017
 		C.	6993
 		D.	7045
Would it be B?

anonymous · Answer

a1=21
d=a2-a1=?
n=1000
calculate an

anonymous · Answer

ok im kinda lost?

freckles · Answer

first what is your common difference @tallan ?

freckles · Answer

@surjithayer was saying to find the common difference take a term from your sequence and subtract the previous term
can you do that?

freckles · Answer

for example
what is 31-24
or 38-31
or 45-38
or 52-45
these differences should all be the same since this is arithmetic sequence
so you only need to find one of those differences

freckles · Answer

to determine the value of d

anonymous · Answer

i got it thanks!! The answer is B.. But I do have another question... could you help me on it?

freckles · Answer

sure I can try

anonymous · Answer

Which of the following choices is the simple formula for the nth term of the following arithmetic sequence?

5, 1, -3, -7, -11, ...

anonymous · Answer

A.	4n + 1
 		B.	4n + 9
 		C.	5n + 4
 		D.	-4n + 1
 		E.	-4n + 9

freckles · Answer

well let's look at the form $$a_n=a_1+d(n-1)$$
d is the common difference 
a_1 is the first term of your sequence

--
to find d; just take a term and subtract its previous term
a_1 should be pretty easy to see (After all it is the first number in the sequence)

freckles · Answer

we will enter these two numbers into the formula above

freckles · Answer

then do a little distributing and combining like terms

freckles · Answer

$$a_n=a_1+dn-d \ a_n=dn+(a_1-d)$$
that is you will be able to find a1-d

freckles · Answer

have you found the common difference yet?

anonymous · Answer

im really slow at math so im trying to figure it out @freckles

freckles · Answer

again to find the common difference
take a term and then subtract it's previous term
so you perform anyone of the differences:
1-5
-3-1
-7-(-3)
-11-(-7)

anonymous · Answer

-4?

freckles · Answer

so replace d with -4 and replace a1 with 5

anonymous · Answer

ok hold on

anonymous · Answer

9?

freckles · Answer

$$a_n=a_1+dn-d \ a_n=dn+(a_1-d) \ a_n=-4n+9$$
a1-d is definitely 9 :)

anonymous · Answer

Thank you so much for your help!!!

freckles · Answer

np