A Series is the addition of successive terms in such a way that they are related to another according to a well defined rule. In other words, series is the addition of a sequence.
Examples of series are;
2 + 5 + 8 + 11 + 14 + ……..
4 + 16 + 64 + 256 + 1024 + ………
-1 + 0 + 7 + 14 + 23 + 34 + ……..
Note
Just like sequence you will be given what you’ll know as nth
term formula to find the terms of series and the formula always differ per
questions.
Examples;
1. Find the series of the first six terms of 2n +
4n2.
Solution
Note
2n + 4n2 stands as a formula that
you’ll use to solve for the first six terms mentioned in the question. Finding the
first six terms means solving for T1, T2, T3, T4,
T5 and T6 respectively.
Step 1
Tn = 2n + 4n2 ---The nth
term formula.
T1 = 21 + 4(1)2
T1 = 2 + 4(12)
T1 = 2 + 4(1)
T1 = 2 + 4
T1 = 6
Step 2
T2 = 22 + 4(2)2
T2 = 4 + 4(22)
T2 = 4 + 4(2 × 2)
T2 = 4 + 4(4)
T2 = 4 + 4 × 4
T2 = 4 + 16
T2 = 20
Step 3
T3 = 23 + 4(3)2
T3 = 8 + 4(32)
T3 = 8 + 4(3 × 3)
T3 = 8 + 4(9)
T3 = 8 + 36
T3 = 44
Step 4
T4 = 24 + 4(4)2
T4 = 16 + 4(42)
T4 = 16 + 4(4 × 4)
T4 = 16 + 4(16)
T4 = 16 + 64
T4 = 80
Step 5
T5 = 25 + 4(5)2
T5 = 32 + 4(52)
T5 = 32 + 4(5 × 5)
T5 = 32 + 4(25)
T5 = 32 + 100
T5 = 132
Step 6
T6 = 26 + 4(6)2
T6 = 64 + 4(62)
T6 = 64 + 4(6 × 6)
T6 = 64 + 4(36)
T6 = 64 + 144
T6 = 208
The series of the first six terms will be; 6 +
20 + 44 + 80 + 132 + 208 +…
2. Find the sum of the series n2 + 5n up to the 4th
term.
Solution
Step 1
Tn = n2 + 5n---Formula
T1 = 12 + 5(1)
T1 = 1 + 5
T1 = 6
Step
2
T2 = 22 + 5(2)
T2 = 4 + 5 × 2
T2 = 4 + 10
T2 = 14
Step
3
T3 = 32 + 5(3)
T3 = 9 + 5 × 3
T3 = 9 + 15
T3 = 24
Step
4
T4 = 42 + 5(4)
T4 = 16 + 5 × 4
T4 = 16 + 20
T4 = 36
The sum of the series will be; 6 + 14 + 24 +
36 = 80.
Practice these questions below;
1. What is the sum of the eight series of an nth term equals 2n
+ 5n?
2. Find the seven series of the term (n + 1)2 – 2n.
3. Write out the series of the term 3n(n – 1).
4. Find the series of the first five terms of n(2 + 3n).
5. Find the sum of the series 5(3n - 1) up to the 4th
term.
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