Question
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!!
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!!
Answers
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 = 11-8d
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
11-7=4
all is good
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 = 11-8d
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
11-7=4
all is good
Anonymous
The third term of an arithmetic sequence is 15, and the fifth term is 37. What is the first term?