Zadanie 9a
Express a₁ in terms of r.
Convergent geometric totals
Recognize the convergence condition for a geometric series and calculate its infinite total.
Tę umiejętność sprawdza 7 zadań wzorowanych na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 7 Otwórz w wyszukiwarce z filtrami
Zadanie 9c
(i) Show that 69r2 − 98r + 29 = 0. (ii) Find r. (iii) Hence find a₁.
Zadanie 8b
Now set k = −6. (i) Prove that the three terms form the start of a geometric sequence. (ii) Explain why the corresponding infinite geometric series has no finite sum.
Zadanie 9c
Show that a run starting at height x has total travel distance d = 7x.
Zadanie 9d
Write down d1.
Zadanie 9e
The stage crosses the reference mark at T,2T,3T,… . Let uₙ be its greatest distance from the mark during (n−1)T<t<nT. These distances form a geometric sequence. Find (i) its common ratio; (ii) the total distance travelled if the model continues indefinitely.
Zadanie 8a
Suppose it is geometric. (i) Show that . (ii) For p>0 and infinite sum , find x.