Zadanie 7c
For the arithmetic sequence find (i) the first term; (ii) the common difference; (iii) the nth term.
Arithmetic patterns and totals
Determine terms and finite totals of equally spaced sequences, use sigma notation, and interpret arithmetic models in context.
Tę umiejętność sprawdza 37 zadań wzorowanych na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 37 Otwórz w wyszukiwarce z filtrami
Zadanie 7d
Find the smallest positive integer n for which Aₙ>Gₙ.
Zadanie 9d
Prove that cₙ is arithmetic.
Zadanie 9e
Find the largest integer k for which C₂₄<0.
Zadanie 8a
The first three assemblies are shown. Write down t3.
- Materiał graficzny
Zadanie 8b
Find t4.
Zadanie 8c
Show that .
Zadanie 8d
Rods are supplied in boxes of 50. Find the maximum number of tiers that can be built using 12 boxes.
Zadanie 8e
A complete assembly uses a whole number of boxes with no rods left over. Find its smallest possible positive number of tiers.
Zadanie 8f
Each rod is 12 cm long. Find the minimum number of rods needed for an assembly whose height exceeds 2.5 m. Ignore rod thickness.
Zadanie 8a
Assume the sequence is arithmetic. (i) Find k. (ii) Hence or otherwise, find u3.
Zadanie 9e
Run 2 starts at 11.6 m. The 20 values d1, d2, …, d20 form an arithmetic sequence. Which run is the first to have total travel below 40 m?
Zadanie 2a
Find its 23rd term.
Zadanie 2b
The sum of its first n terms is zero, where n is a positive integer. Find n.
Zadanie 3
An arithmetic sequence satisfies u8 = 15 and u5 + u13 = 40. Find its first term and common difference.
Zadanie 7a
For Fund A: (i) find the monthly credit to two decimal places; (ii) find the yearly credit; (iii) write its balance after n years as 6000+pn; (iv) show that its balance after 5 years is USD 6990.
Zadanie 1a
Find the common difference.
Zadanie 1b
Find an expression for its nth term uₙ.
Zadanie 9a
Show that 2p − q = a.
Zadanie 9c
Show that p>2.
Zadanie 9d
Suppose a=16 and s>0. List the first four terms of (i) the arithmetic sequence; (ii) the geometric sequence.
Zadanie 9e
Suppose a=16 and s>0, and define un = An + ln Gn. (i) Show that u_n is arithmetic and find its common difference. (ii) Show that .
Zadanie 6
An arithmetic sequence satisfies u6 = 24 and S15 = 240. Find k for which uk = 0.
Zadanie 6
An arithmetic sequence satisfies u8 = 21 and S19 = 285. Find the positive integer k for which uk = 0.
Zadanie 2a
Find the common difference.
Zadanie 2b
Find k.
Zadanie 8a
(i) Find S_5. (ii) Given S_6=90, find u_6.
Zadanie 8b
Find u_1.
Zadanie 8c
Hence or otherwise, express u_n in terms of n.
Zadanie 4a
Find p and q.
Zadanie 4b
Find the fifth term.
Zadanie 4a
Find p and q.
Zadanie 4b
Find the fifth term.
Zadanie 2a
State u₁.
Zadanie 2b
Given uₙ=−38, find n.
Zadanie 2c
Find the common difference.
Zadanie 8b
Now suppose it is arithmetic. (i) Show that p=3/4. (ii) Express the common difference d as a rational multiple of ln x. (iii) The sum of the first n terms is −(9/2)ln x. Find n.