Sequences & Series Topic Assessment
(3. i) A geometric series has first term 2 and common ratio 0.2. Find
The 3rd term - ANS a = 2
r = 0.2
a₃ = 2 * 0.2²
a₃ = 0.08
\(3. ii) A geometric series has first term 2 and common ratio 0.2.
The sum of the first 4 terms of the series - ANS
\(3. iii) A geometric series has first term 2 and common ratio 0.2.
The sum to infinity of the series - ANS s(infinity) = a/(1-r)
2/(1-0.2)
2.5
\(4) A geometric series has 1st term 3 and sum to infinity 8. Find the common ratio - ANS
a = 3, S(inifnity) = 8
S(infity) = a/1-r
8 = 3/(1-r)
8(1-r) = 3
1-r = 3/8
r = 1 - 3/8
r = 5/8
\(5. i) A geometric series has first term 54 and 4th term 2
What is the common ratio - ANS 2=54(r³)
r³ = 1/27
r = 1/3
\(5. ii) Geometric: a =54, d= 1/3
Find the sum to infinity of the series - ANS S(infinity) = a/(1-r)
S(infinity) 54/1-1/3
S(infinity) 81
\(5. iii) Geometric: a =54, d= 1/3, Sinfinity = 81
After how many terms is the sum of the series greater than 99% of the sum to infinity? -
ANS ✵99/100 * 81 = 80.19
✵Sn = a(1-r^n)/ 1-r
80.19 < 54(1-(1.3)^n)/ 1- 1/3
✵54(1-(1/3)^n) > 53.46/54
(1/3)^n < 0.01
nlog(1/3) <log0.01
n>log0.01/log1/3
n > 4.191
\(6. i)When Mirka is 5 years old, her parents start to give her pocket money of 50p per
week. On her birthday each year, her parents increase her pocket money by 50p
(3. i) A geometric series has first term 2 and common ratio 0.2. Find
The 3rd term - ANS a = 2
r = 0.2
a₃ = 2 * 0.2²
a₃ = 0.08
\(3. ii) A geometric series has first term 2 and common ratio 0.2.
The sum of the first 4 terms of the series - ANS
\(3. iii) A geometric series has first term 2 and common ratio 0.2.
The sum to infinity of the series - ANS s(infinity) = a/(1-r)
2/(1-0.2)
2.5
\(4) A geometric series has 1st term 3 and sum to infinity 8. Find the common ratio - ANS
a = 3, S(inifnity) = 8
S(infity) = a/1-r
8 = 3/(1-r)
8(1-r) = 3
1-r = 3/8
r = 1 - 3/8
r = 5/8
\(5. i) A geometric series has first term 54 and 4th term 2
What is the common ratio - ANS 2=54(r³)
r³ = 1/27
r = 1/3
\(5. ii) Geometric: a =54, d= 1/3
Find the sum to infinity of the series - ANS S(infinity) = a/(1-r)
S(infinity) 54/1-1/3
S(infinity) 81
\(5. iii) Geometric: a =54, d= 1/3, Sinfinity = 81
After how many terms is the sum of the series greater than 99% of the sum to infinity? -
ANS ✵99/100 * 81 = 80.19
✵Sn = a(1-r^n)/ 1-r
80.19 < 54(1-(1.3)^n)/ 1- 1/3
✵54(1-(1/3)^n) > 53.46/54
(1/3)^n < 0.01
nlog(1/3) <log0.01
n>log0.01/log1/3
n > 4.191
\(6. i)When Mirka is 5 years old, her parents start to give her pocket money of 50p per
week. On her birthday each year, her parents increase her pocket money by 50p
