Mathelaureate

Mathelaureate
IBDP Mathematics
Topic –1: Algebra
Sequence and Series
Practice problems
1
2
3
4
5
The general term of an arithmetic sequence is 𝑒𝑛 = 3𝑛 + 4.
[a] Find the first 4 terms of the sequence.
[2]
[b] Find the 50th term of the sequence.
[3]
The general term of an arithmetic sequence is 𝑒𝑛 = 11 βˆ’ 4𝑛 .
[a] Find the first term and common difference
[2]
[b] Find the 20th term
[3]
Consider the sequence 2, 6, 10, 14, . . . . . . .
[a] Show that it’s an arithmetic sequence
[b] Find the next three terms
[c] Find the expression for the nth term of the sequence
[d] Hence find the 15th term of the sequence
[1]
[1]
[2]
[2]
Consider the arithmetic sequence 20, 17, 14, 11, . . . . . .
[a] Find the common difference
[1]
[b] Find the 10th term of the sequence.
[2]
[c] Given that 𝑒𝑛 = βˆ’37 , find 𝑛.
[3]
Given that 16th term in an arithmetic sequence is 44 and the common difference is 3.
[a] Find the first 4 terms of the sequence.
[2]
[b] Find the 51st term of the sequence.
[3]
[c] Find the sum of first 20 terms of the sequence.
[3]
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6
In an arithmetic sequence 𝑒10 = 43 and 𝑒33 = 204 find the first term and the common
difference.
[5]
7
Find the sum of the series 11 + 18 + 25+ . . . . . . . . . . . . + 74
[5]
8
In an arithmetic sequence the first term is 3 and the 25th term is 51. Find the sum of the
first 30 terms of the sequence.
[6]
9
In an arithmetic sequence the first term is 16, nth term (𝑒𝑛 ) is 81 and the sum of the first
𝑛 terms (𝑆𝑛 ) is 679. Find the number of terms (𝑛) in the sequence.
[6]
10
In an arithmetic sequence 10th term is 109 and 38th term is 389.
[a] Find the first term and the common difference.
[3]
[b] Find the 20th term of the sequence.
[3]
11
In an arithmetic sequence 𝑒14 = βˆ’52 and 𝑒40 = βˆ’156. Find the sum up to 50 terms of
the series.
[6]
12
In an arithmetic sequence 𝑒1 = βˆ’38 , 𝑒𝑛 = βˆ’478 and 𝑆𝑛 = βˆ’11610 , find the number
of terms 𝑛.
[6]
13
Express the following sigma notation in expanded (series) form. Do not find the sum.
10
[π‘Ž]
[𝑐 ]
20
βˆ‘(3𝑛 + 5)
[𝑏]
βˆ‘(9 βˆ’ 10π‘˜)
𝑛=1
π‘˜=1
15
10
βˆ‘(3𝑖
βˆ’ 5)
[𝑑]
𝑖=1
IBDP Math/ Sequence & series / D. J
9 5𝑗
βˆ‘( βˆ’ )
4 2
[4]
𝑗=1
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14
Evaluate the sum of the following expressions.
10
[π‘Ž]
50
[𝑏]
βˆ‘(2𝑛 + 7)
𝑛=1
15
βˆ‘(4𝑛 βˆ’ 3)
[6]
𝑛=1
Find the missing terms in each of the following geometric sequence.
[a] _____ , 1 , _______ , 9
[b] _____ , 4 , _______ , 36
[c] 3, _____ , _____ , _____ , 48
[d] 2 , _____ ,_____ ,_____ ¸162
[4]
16
17
In a geometric sequence the first term is 5 and the common ratio is 2.
[a] Find the 10th term.
[2]
[b] Find the sum up to 7 terms.
[3]
First three terms of a sequence are 4 , 8 , 16
[a] show that it is a geometric sequence
[b] Find the next three terms
[c] Find the general term expression
[d] hence find the 10th term of the sequence
18
The first three terms of a geometric sequence are 250, 50, 10 . . .
[a] Show that sum up to infinity exist for this sequence
[b] Find the next three terms
[c] Find the sum up to infinity of the sequence.
19
The first three terms of a series are βˆ’27 + 9 βˆ’ 3+ . . . . . . . . . ..
[a] Show that this is a infinite geometric series
[b] Find the 7th term of the series
[c] Find the sum of first 7 terms of the series
[d] Find the sum of the first 10 terms of the series
[e] Find the sum up to infinity of the series.
IBDP Math/ Sequence & series / D. J
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20
In a geometric sequence 𝑒1 = 3 , and 𝑒4 = 375.
[a] Find the common ration β€˜ r β€˜ .
[b] Find the 8th term of the sequence
[c] Find 𝑆7 .
IBDP Math/ Sequence & series / D. J
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