Question

The tenth term of an arithmetic sequence is
37
2
,
and the second term is
5
2
.
Find the first term. Can someone help?

Answer 1

*37/2 and 5/2

Answer 2

for any arithmetic series
An = A1 + (n-1)*d
A10 = 37/2 = A1 +(10-1)*d
-> 37/2 = A1 + 9d
-> A1 = 37/2 - 9d
To solve for d use second term and substitute in for A1
A2 = 5/2 = (37/2 -9d) +(2-1)d
->5/2 = 37/2 -8d
->(5-37)/2 = -8d
->-16 = -8d
->2=d
substitute for back in for d to find A1
A1 = 37/2-9(2)
=37/2 - 18
=37/2 - 36/2 = 1/2