
UNIT
10 :
SEQUENCES AND SERIES
LESSON 3:
ARITHMETIC SERIES HOMEWORK QUESTIONS
Quick Review
Arithmetic
Series:
Recall a sequence such as –2, 3, 8, 13, …
is called an Arithmetic Sequence.
These sequences have the following properties.
·
Terms
are denoted as t_{1} , t_{2} , t_{3 , }referring
_{ }to term1, term 2,
term 3 …
·
The difference between successive terms is constant. ie t_{2}
– t_{1} = t_{3} – t_{2} = t_{4} – t_{3}
etc
·
This
difference is called the common
difference and denoted
using the letter d. Here d
= 5.
·
The
first term is denoted using the letter a. Here a = 2.
·
Successive
terms are found by adding the common difference, d, to the preceding
term. Hence t_{5} = 13 +
5 = 18 etc.
·
The
formula for the general term or nth term is t_{n }= a + (n
– 1)d
·
Arithmetic
sequences are linear functions with domain the natural numbers N =
{1, 2, 3, 4, 5, …}
Definition: The sum of the terms of an
arithmetic sequence is an Arithmetic Series.
Homework
Questions:
1. Find the sum of the following arithmetic
series.
2. In each of the following arithmetic series,
determine S_{60} .
a) 3 + 7 + 11 + …
b) 11 +
(2) + 5 + 12 + …
c) 2 +
2.5 + 3 + …
3. For each of the following series, the first
and last terms are given. Find the sum
in each case.
5. Find the number of terms in each series
below having the given sum.
6. For a certain arithmetic series, t_{5}
= 16 and S_{20} = 650.
find a and d.
7. Find the first term and common difference
for the sequence defined by t_{n}
= 5 – 2n. Find S_{40}.
8. On the first day of practice, the track team
ran 3 laps of the field. The coach
plans to increase the number of laps by two each practice. How many laps will they run on the eleventh
practice? How many laps have they run
in total after the 11^{th} practice?
10. The first term of an arithmetic series is –
15. The sum of the first 16 terms is
480. Find the common difference and the
first 4 terms.
11. The first term of an arithmetic series is –
4. The sum of the first 15 terms is
1365. Find the common difference and
the sum of the first 25 terms.
Solutions:
1. Find the sum of the following arithmetic
series.
Solutions:
a = 1 d = 3 n = ? t_{n} = 100 S_{n} = ?
a = 255 d = 4 n = ? t_{n} = 3 S_{n} = ?
a = 3 d = 4 n = ? t_{n} = 175 S_{n} = ?
2. In each of the following arithmetic series,
determine S_{60} .
a) 3 + 7 + 11 + …
b) 11 +
(2) + 5 + 12 + …
c) 2 +
2.5 + 3 + …
Solutions:
a) 3 + 7 + 11 + …
a = 3 d = 4 n = 60 S_{60} = ?
a = 11 d = 7 n= 60 S_{60} = ?
b) 11 +
(2) + 5 + 12 + …
c) 2 +
2.5 + 3 + …
a = 2 d = 0.5 n = 60 S_{n} = ?
3. For each of the following series, the first
and last terms are given. Find the sum
in each case.
a = 8 l = ? n = 11 S_{n} = ?
Solutions:
a =  4 l = 29 n = 12 S_{n} =?
a = 11 n = 9 l = 13 S_{n} =?
a = 10.5 n = 10 l = 3 S_{n} = ?
a = 21 d = 7 n = ? t_{n} = 147 S_{n} = ?
5. Find the number of terms in each series below
having the given sum.
Solutions:
6. For a certain arithmetic series, t_{5}
= 16 and S_{20} = 650.
find a and d.
Solution:
7. Find the first term and common difference
for the sequence defined by t_{n}
= 5 – 2n. Find S_{40}.
Solution:
8. On the first day of practice, the track team
ran 3 laps of the field. The coach
plans to increase the number of laps by two each practice. How many laps will they run on the eleventh
practice? How many laps have they run
in total after the 11^{th} practice?
Solution:
This
forms an arithmetic sequence(series) with first term 3 and common difference
2. Find t_{11}.
a = 48 d =  4 n = 9
10. The first term of an arithmetic series is –
15. The sum of the first 16 terms is
480. Find the common difference and the
first 4 terms.
Solution
11. The first term of an arithmetic series is –
4. The sum of the first 15 terms is
1365. Find the common difference and
the sum of the first 25 terms.
Solution: