Question

find the 55'th term of the arithmetic sequence 11, 30, 49...

Answer 1

To find the 55th term of an arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n-1)d

Where:
a_n is the nth term
a_1 is the first term
d is the common difference between terms
n is the term number

In this case, the first term (a_1) is 11 and the common difference (d) is 30 - 11 = 19.

So the formula to find the nth term is:
a_n = 11 + (n-1)19

Now, substitute n = 55 into the formula to find the 55th term:
a_55 = 11 + (55-1)19
a_55 = 11 + 54(19)
a_55 = 11 + 1026
a_55 = 1037

Therefore, the 55th term of the arithmetic sequence is 1037.