Question

determine the 6th and 20th terms of the arthimetic sequence 50,46,42,38..

Answer 1

To find the 6th term of the arithmetic sequence, we use the formula for the general term of an arithmetic sequence:

a_n = a_1 + (n-1)d

where:
a_n is the nth term of the sequence
a_1 is the first term of the sequence
d is the common difference
n is the position of the term we want to find

In this case, the first term (a_1) is 50, the common difference (d) is -4 (since each term decreases by 4), and we want to find the 6th term (n = 6).

a_6 = 50 + (6-1)(-4)
a_6 = 50 + 5(-4)
a_6 = 50 - 20
a_6 = 30

So, the 6th term of the sequence is 30.

To find the 20th term of the arithmetic sequence, we use the same formula but with n = 20:

a_20 = 50 + (20-1)(-4)
a_20 = 50 + 19(-4)
a_20 = 50 - 76
a_20 = -26

So, the 20th term of the sequence is -26.