Zadanie 1b
Use the arithmetic-sequence sum to show that T1(n) = n2 + 2n.
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 39 zadań wzorowanych na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 39 Otwórz w wyszukiwarce z filtrami
Zadanie 7b
Find the greatest possible value of Sn, to two decimal places.
Zadanie 10a
The first three assemblies are shown. Write down t3.
- Materiał graficzny
Zadanie 10b
Find t4.
Zadanie 10c
Show that .
Zadanie 10d
Rods are supplied in boxes of 50. Find the maximum number of tiers that can be built using 12 boxes.
Zadanie 10e
A complete assembly uses a whole number of boxes with no rods left over. Find its smallest possible positive number of tiers.
Zadanie 10f
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 10a
Assume the sequence is arithmetic. (i) Find k. (ii) Hence or otherwise, find u3.
Zadanie 1a
Find its 23rd term.
Zadanie 1b
The sum of its first n terms is zero, where n is a positive integer. Find n.
Zadanie 1
An arithmetic sequence satisfies u8 = 15 and u5 + u13 = 40. Find its first term and common difference.
Zadanie 10a
Show that 2p − q = a.
Zadanie 10c
Show that p>2.
Zadanie 10d
Suppose a=16 and s>0. List the first four terms of (i) the arithmetic sequence; (ii) the geometric sequence.
Zadanie 10e
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 5
An arithmetic sequence satisfies u8 = 21 and S19 = 285. Find the positive integer k for which uk = 0.
Zadanie 2a
Show that L(x) = 2x + 8 is admissible.
Zadanie 2b
(i) Show that r=−c/m. (ii) For admissible L, show that L(x) = mx + 2m2/(m − 1). (iii) State the further excluded value of m.
Zadanie 2c
Exactly three admissible L have integer r,m,c. One is L(x) = 3x + 9. Use the general expression to find the other two. For an admissible linear function, c = 2m2/(m − 1) and r = −c/m, with m ≠ 0, 1.
Zadanie 2e
For an admissible cubic F: (i) express r2 − r1 in terms of a,b; (ii) use the sum and difference of the stationary abscissas to show that r1 = (3a2 − 3ab − 2b)/(6a); (iii) use this result to show that b=0 or a=−1/3.
Zadanie 2f
Determine the two admissible cubic functions with b=0.
Zadanie 2g
Now set a=−1/3. (i) Express r₁ in terms of b. (ii) Hence or otherwise find the exact pairs (b,c) making F admissible. Give each value as a rational expression involving a square root.
Zadanie 10a
(i) Find S_5. (ii) Given S_6=90, find u_6.
Zadanie 10b
Find u_1.
Zadanie 10c
Hence or otherwise, express u_n in terms of n.
Zadanie 12d
Hence prove that the areas R_1,R_2,… form an arithmetic sequence.
- Materiał graficzny
Zadanie 3a
Find p and q.
Zadanie 3b
Find the fifth term.
Zadanie 3a
Find p and q.
Zadanie 3b
Find the fifth term.
Zadanie 1a
(i) Verify algebraically that C1(n) = n(n − 1) + 1. (ii) The count 421 occurs in this r=1 scheme. Determine its index n.
Zadanie 1d
For r=17 the counts may be written C17(n) = 1 + 34 + 68 + ⋯ + 34(n − 1), with just 1 at n=1. Use an arithmetic-series sum to show that C17(n) = 17n(n − 1) + 1.
Zadanie 1e
Using tables or another suitable method, find the smallest count greater than 1 that occurs in both the r=1 and r=17 schemes.
Zadanie 1a
State u₁.
Zadanie 1b
Given uₙ=−38, find n.
Zadanie 1c
Find the common difference.
Zadanie 10b
Now suppose the series is arithmetic with common difference d. (i) Show that p=3/4. (ii) Write d as a rational multiple of ln x. (iii) If the sum of its first n terms is , find n.
Zadanie 1a
Show that S1(n) = n2.