Posted by Max on .
The sum of the 4th and the 14th term of an arithmetic sequence equals 22. The 9th term is 4 larger than the 4th term. Calculate the first term of the sequence.
I've been trying to solve this for like an hour but I just can't figure out how to do it! I'd really appreciate your help! Thanks!!

Math  Arithmetic Sequences 
Reiny,
"The sum of the 4th and the 14th term of an arithmetic sequence equals 22" > a+3d + a+13d = 22
2a + 16d = 22
a + 8d = 11 (#1)
"The 9th term is 4 larger than the 4th term" > a+8d  (a+3d) = 4
5d = 4
d = 4/5
a = 118d
a = 11  8(4/5) = 23/5
check:
t4 = 23/5 + 3(4/5) = 35/5 = 7
t9 = 23/5 + 8(4/5) = 55/5 = 11
t14 = 23/5 + 13(4/5) = 75/5 = 15
11+15 = 22
117=4
all is good 
Math  Arithmetic Sequences 
Anonymous,
The third term of an arithmetic sequence is 15, and the fifth term is 37. What is the first term?