Arithmetric sequence

Question

First term of sequence is 3 and the common difference is 5. The nth term is the first term in this sequence >1000. Find value of n.

Answer 1

a_n = a₁ + (n - 1)d

1000 < 3 + (n - 1)5

997 < 5n - 5

1002 < 5n

200.4 < n

 

n would be 201.

Answer 2

this sequence starts off:  3,8,13,18...

we are interested in the first number in this sequence greater than 1000.

if the first term were 0 then (1000/5=200) the 200th term would be 1000 and the first number in the sequence greater than 1000 would be 1005 and would be the 101st term

But we started at 3 so the 201st term is 1003 and n=201

 

 

There are formal ways to arrive at the answer but this is a simple approach

 

Hope this is clear and helps

 

rich

Answer 3

Since the sequence has a common difference, it is an arithmetic sequence.  The explicit form of the sequence is:

 

(first term) + (common difference)(n-1) = a_n

3 + 5(n-1) = a_n

 

We want the value of n for the first term that is > 1000, so set a_n = 1000 and solve for n:

 

3 + 5(n-1) > 1000

3 + 5n - 5 > 1000

5n - 2 > 1003

5 n > 1002

 

n > 200.4

 

Since n must be an integer, the first term that is > 1000 will be n = 201.