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UNIT
8 :
SEQUENCES AND SERIES
LESSON 7:
UNIT 8 TEST SOLUTIONS
1. In
each of the following tn is given.
Find the first 4 terms and t12.
Solution:
2. Find tn, t15 and S15 for each of the following series:
Solution: Solution:
a = 3 d = -4 tn = ? n = 15 t15 = ? S15 = ? a = 2 d = 7 tn = ? n = 15 t15 = ? S15 = ?
3. Find tn, t8 and S8 for each of the following series:
Solution:
a = 2 r = 3 tn = ? t8 = ? S8 = ? a = 3 r = - 4 tn = t8 = S8 =
4. Determine whether each sequence is
arithmetic, geometric, or neither.
a) 4, 1, -2, -5,
b) 1, 3, 33, 333,
c) -2, 6, -18, 54,
d) 4, 3.6, 3.2, 2.8,
e) 1, 4, 9, 16,
f) 81, -27, 9, -3,
Solutions:
5. Find the sum of each series.
Solutions:
a = -54 d = 7 n = ? tn = 51 Sn = ? a = 4 r = -3 n = ? tn = - 8748 Sn = ?
6. The first term of an arithmetic sequence is
2 and the sum of the first five terms is 40.
Find the first five terms and tn.
Solution:
7. The fourth and eighth terms of a geometric sequence of positive numbers are Ό and 4 respectively. Find the seventh term and the sum of 12 terms.
Solution:
8. The sum of the first four terms of a
positive geometric series is 60. The
fourth term is 4 times the second term.
Find the first four terms.
Solution:
9. An new internet company Rebus.com made a
profit of $120 000 this year. If
profits increase by 5% for each of the next 6 years, what will be the total
profit made by the company so far ?
Solution:
This years profit is 120 000
1st year following profit will be 120 000(1.05)1
a = 120 000 r = 1.05 n = 7 S7 = ?
2nd year following profit will be 120 000(1.05)2
.
.
.
6th year following profit will be 120 000(1.05)6
Series is 120 000 + 120 000(1.05)1 + 120 000(1.05)2 + + 120 000(1.05)6
Find S7 for this series.
10. Explain the difference between a sequence and a series.
Solution:
A sequence is a set of numbers arranged according to a pattern or order.
A series is the sum of the terms of a sequence.
