SOLUTION: Hello,can anyone help me with these series and sequences questions? I have a test on them tomorrow and I'm struggling with these questions about Arithmetic Progression: 1. The 5

Question 425758: Hello,can anyone help me with these series and sequences questions? I have a test on them tomorrow and I'm struggling with these questions about Arithmetic Progression:
1. The 5th and 11th terms of Arithmetic Progression are 7 and 61 respectively. Find the common difference and the 1st term.
2. The 1st term of a Arithmetic Progression is -3 and the 15th term is 53. Find the common difference.
3. The sum of the 7th and 9th terms of an Arithmetic Progression is 52 and the sum of the 5th and 16th terms 67. Find the 1st term and the common difference.
Thank you!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. The 5th and 11th terms of Arithmetic Progression are 7 and 61 respectively. Find the common difference and the 1st term.
General formula for the nth term
of an arithmetic sequence: a(n) = a(1)+(n-1)d
--------
5th term: 7 = a(1) + 4d
11th ter:61 = a(1)+ 60d
----
Subtract and solve for "d":
54 = 54d
d = 1 (common difference)
---
Solve for a(1):
7 = a(1) + 4*1
a(1) = 3 (the 1st term in the progression)
---------------------

2. The 1st term of a Arithmetic Progression is -3 and the 15th term is 53. Find the common difference.
---
a(1) = -3
15th: a(1) + 14(d) = 53
-3 + 14d = 53
14d = 56
d = 4 (common difference)
----------------------------------------------

3. The sum of the 7th and 9th terms of an Arithmetic Progression is 52 and the sum of the 5th and 16th terms 67. Find the 1st term and the common difference.
---
7th: a(1)+6d
9th: a(1)+8d-
---
Sum: 2(a(1))+14d = 52
---
5th: a(1) + 4d
16th:a(1) +15d
Sum = 2(a(1))+19d = 67
---
Subtract to get:
5d = 15
d = 3 (common difference)
---
Solve for "a(1)"
2(a(1)) + 14d = 52
2(a(1)) + 42 = 52
2(a(1)) = 10
a(1) = 5 (1st term)
========================
Cheers,
Stan H.
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