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MATHEMATICS
MATH Q1
1.5 SERIES - ARITHMETIC AND GEOMETRIC
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Cards (15)
Sₙ -
Sum of all n terms
Write the formula for Sₙ in an Arithmetic Series.
Note:
Write subscript like aₙ as [an]. For example, a₅ we write it as a5.
For Fractions, instead of writing ½, write 1/2 instead.
For Exponents, we use [^]. For example, a⁴ can be written as a^4.
Sn = n/2(a1 + an)
Find the 20th term and the sum of the first 20 terms of the arithmetic sequence -7, - 4, -1, 2, …
a1 =
-7
n =
20
d =
3
an =
50
Sn =
430
Find the 25th term and the sum of the first 25 terms of the arithmetic sequence 12, 16, 20, 24, …
a1 =
12
n =
25
d =
4
an =
108
Sn =
1500
Find four arithmetic means between 16 and 76.
a1 =
16
n =
6
an =
76
d =
12
16
,
28
,
40
,
52
,
64
,
76
Find the sum of the first 30 terms of the arithmetic sequence 11, 16, 21, 26, …
a1 =
11
n =
30
d =
5
an =
156
Sn =
2505
Write the formula for Sn in a Geometric Sequence.
Note:
Write subscript like aₙ as [an]. For example, a₅ we write it as a5.
For Fractions, instead of writing ½, write 1/2 instead.
For Exponents, we use [^]. For example, a⁴ can be written as a^4.
Sn =
a1(1-r^n)/1-r
Find the sum of the first 12 terms of the geometric sequence 3, -9, 27, -81, 243, ...
a1 =
3
n =
12
r =
-3
Sn =
-398580
Find S10 of the Geometric Sequence -1/2, -1, -2, -4...
a1 =
-1/2
n =
10
r =
2
Sn =
-511.5
or
-511
1/2
Arithmetic Series
- The sum of first n terms in an arithmetic sequence.
Finite Geometric Series
- The sum of first 𝑛 terms in a geometric sequence.
Infinite Geometric Series
- The sum of infinite terms of a geometric sequence.
Formula for infinite geometric series
Note:
Write subscript like aₙ as [an]. For example, a₅ we write it as a5.
For Fractions, instead of writing ½, write 1/2 instead.
For Exponents, we use [^]. For example, a⁴ can be written as a^4.
S∞ =
a1/1-r
Find the sum of the Geometric Sequence: 1, 1/2, 1/4, 1/8, 1/16, ...
a1 =
1
r =
1/2
S∞ =
2
Find the sum of the Geometric Sequence: 2, 2/3, 2/9, 2/7...
a1 =
2
r =
1/3
S∞ =
3