Page 102 - Mathematics_Form_3

Sequences and series

2. The first term of an arithmetic (c) the value of S given that
n
progression is 6 and the common A = 19 and d = − 2.
1
difference is 1.5. If the sum of the 9. Find three consecutive terms of an
first n terms is 90, find the number AP whose sum and product are 24
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of terms of the progression.
and 440, respectively.
3. If Ali earns a salary of 1,256,000
10. The ratio of the sum of the first 10
Tanzanian shillings per month and
terms to the sum of the first 20 terms
his annual increment is 45,500
of an AP is 1:4. Find the ratio of the
Tanzanian shillings, determine:
first term to the common difference.
(a) his monthly earning during the
16 year of employment. 11. If the sum of the first p terms of an
th
(b) his total earning after 18 years. AP is equal to the sum of its first

4. The first term of an arithmetic q terms, prove that the sum of its
progression is − 12 and the last term first (pq+ ) terms is zero. Provided
is 40. If the sum of n terms is 196, that p ≠ q .
find the number of terms and the 12. The sum of the first n terms of an
common difference. AP is 4 ² 7.n + n Find its 10 term.
th
5. The first term of an arithmetic 13. The sum of the first n terms of an AP
progression is 13 and the fifth term is given by S = 5n + 3n. Find the
2
n
is 21. Find the common difference first term and common difference.
and the sum of the first ten terms.

6. Find the difference between the
Arithmetic mean
sum of the first five terms of two
arithmetic progressions whose If a, M and b are three consecutive
first terms are 12 and 8, and their terms of an arithmetic progression, the
common differences are 2 and 3, common difference equals to M − a
respectively. or b − M .
7. How many integers are there Thus, M − a = b − M Mathematics for Secondary Schools
between 14 and 1,000 which are 2M = a + b , or
divisible by 17? a + b

M = _____ .
8. Find: 2
(a) A and S , given that A = 40 Therefore, the arithmetic mean of a and
1 9 9 a + b
_____
and d = 4. b is M = 2 .
(b) d given that A = 2 and In other words, the arithmetic mean M
1
S = 100. is the average of terms a and b.
10

Student\s Book Form Three 95

18/09/2025 09:59:23
MATHEMATIC F3 SB.indd 95 18/09/2025 09:59:23
MATHEMATIC F3 SB.indd 95