# Math - Arithmetic Sequences

posted by .

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 -

"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

• Math - Arithmetic Sequences -

The third term of an arithmetic sequence is 15, and the fifth term is 37. What is the first term?

## Similar Questions

1. ### arithmetic

An arithmetic n geometric sequence have the same first term 2.with the 2nd term x. the sum of the 3rd term of the AS is equal to the 3rd term of the GS. Give the first 3 terms of both sequences.
2. ### Arithmetic Sequence

Given the third term of an arithmetic sequence less than the fourth term by three. The seventh term is two times the fifth term. Find the common difference and the first term.
3. ### Maths

1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression is …
4. ### math

find the 4th term of an arithmetic sequence whose first term is -8 and whose 9th term is 32.
5. ### Algebra

True or False 1. – 5, – 5, – 5, – 5, – 5, … is an arithmetic sequence. 2. In an arithmetic sequence, it is possible that the 13th term is equal to its 53rd term. 3. In an arithmetic sequence, the common difference is computed …
6. ### math

The 9th term of an arithmetic sequence is 12 and the 17th term is 28, find the 4th term of the arithmetic sequences
7. ### mathematics

1.1 the third term of an arithmetic sequence is 8 and the 15 term is 44 . Calculate: 1.1 the common difference and first term. 1.2 the sum of the first 50 terms. 1.2 1;4;7;10.... Is an arithmetic sequence .find: 1.2.1 the 30 term.
8. ### arithmetic sequence

the 40th term of an arithmetic sequence is equal to the sum of the 20th and 31st term. if the common difference of the sequence is-10. find the first term.
9. ### Algebra

I am so lost on these problems. Write a geometric sequence that starts with 3 and has a common ratio of 5. What is the 23rd term in the sequence. Write an arithmetic sequence that has a common difference of 4 and the eighth term is …
10. ### Math

- If the 4th term of an arithmetic sequence is 24 and the 12th term is 56, whats the first term?

More Similar Questions