Transcript of "11X1 T14 02 geometric series (2010)"
1.
Geometric Series
2.
Geometric Series
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
3.
Geometric Series
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
4.
Geometric Series
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
T
r 2
a
5.
Geometric Series
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
T
r 2
a
T
3
T2
6.
Geometric Series
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
T
r 2
a
T
3
T2
Tn
r
Tn1
7.
Geometric Series
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
T T1 a
r 2
a
T
3
T2
Tn
r
Tn1
8.
Geometric Series
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
T T1 a
r 2
a T2 ar
T
3
T2
Tn
r
Tn1
9.
Geometric Series
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
T T1 a
r 2
a T2 ar
T3 T3 ar 2
T2
Tn
r
Tn1
10.
Geometric Series
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
T T1 a
r 2
a T2 ar
T3 T3 ar 2
T2 Tn ar n1
Tn
r
Tn1
11.
Geometric Series
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
T T1 a
r 2
a T2 ar
T3 T3 ar 2
T2 Tn ar n1
Tn
r
Tn1 e.g.i Find r and the general term of 2, 8, 32,
12.
Geometric Series
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
T T1 a
r 2
a T2 ar
T3 T3 ar 2
T2 Tn ar n1
Tn
r
Tn1 e.g.i Find r and the general term of 2, 8, 32,
a 2, r 4
13.
Geometric Series
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
T T1 a
r 2
a T2 ar
T3 T3 ar 2
T2 Tn ar n1
Tn
r
Tn1 e.g.i Find r and the general term of 2, 8, 32,
Tn ar n1 a 2, r 4
14.
Geometric Series
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
T T1 a
r 2
a T2 ar
T3 T3 ar 2
T2 Tn ar n1
Tn
r
Tn1 e.g.i Find r and the general term of 2, 8, 32,
Tn ar n1 a 2, r 4
24
n1
15.
Geometric Series
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
T T1 a
r 2
a T2 ar
T3 T3 ar 2
T2 Tn ar n1
Tn
r
Tn1 e.g.i Find r and the general term of 2, 8, 32,
Tn ar n1 a 2, r 4
24
n1
22
2 n 1
22
2 n2
16.
Geometric Series
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
T T1 a
r 2
a T2 ar
T3 T3 ar 2
T2 Tn ar n1
Tn
r
Tn1 e.g.i Find r and the general term of 2, 8, 32,
Tn ar n1 a 2, r 4
24
n1
22
2 n 1
Tn 22 n1
22
2 n2
19.
ii If T2 7 and T4 49, find r
ar 7
ar 3 49
20.
ii If T2 7 and T4 49, find r
ar 7
ar 3 49
r2 7
21.
ii If T2 7 and T4 49, find r
ar 7
ar 3 49
r2 7
r 7
22.
ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, … to
ar 7 be greater than 500.
ar 3 49
r2 7
r 7
23.
ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, … to
ar 7 be greater than 500.
ar 3 49 a 1, r 4
r2 7
r 7
24.
ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, … to
ar 7 be greater than 500.
Tn 14
n1
ar 3 49 a 1, r 4
r2 7
r 7
25.
ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, … to
ar 7 be greater than 500.
Tn 14
n1
ar 3 49 a 1, r 4
r2 7 Tn 500
r 7
26.
ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, … to
ar 7 be greater than 500.
Tn 14
n1
ar 3 49 a 1, r 4
r2 7 Tn 500
r 7 4n1 500
27.
ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, … to
ar 7 be greater than 500.
Tn 14
n1
ar 3 49 a 1, r 4
r2 7 Tn 500
r 7 4n1 500
log 4n1 log 500
28.
ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, … to
ar 7 be greater than 500.
Tn 14
n1
ar 3 49 a 1, r 4
r2 7 Tn 500
r 7 4n1 500
log 4n1 log 500
n 1log 4 log 500
29.
ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, … to
ar 7 be greater than 500.
Tn 14
n1
ar 3 49 a 1, r 4
r2 7 Tn 500
r 7 4n1 500
log 4n1 log 500
n 1log 4 log 500
n 1 4.48
n 5.48
30.
ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, … to
ar 7 be greater than 500.
Tn 14
n1
ar 3 49 a 1, r 4
r2 7 Tn 500
r 7 4n1 500
log 4n1 log 500
n 1log 4 log 500
n 1 4.48
n 5.48
T6 1024, is the first term 500
31.
ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, … to
ar 7 be greater than 500.
Tn 14
n1
ar 3 49 a 1, r 4
r2 7 Tn 500
r 7 4n1 500
log 4n1 log 500
n 1log 4 log 500
n 1 4.48
n 5.48
T6 1024, is the first term 500
Exercise 6E; 1be, 2cf, 3ad, 5ac, 6c, 8bd, 9ac, 10ac, 15, 17,
18ab, 20a
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