Sequences and Series: math test, Grade 11

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Math tests Grade 11 : Sequences and Series — Zyro the alien explorer of Planète Maths

Suggested time: 45 minutes. Out of 20 points. Calculator allowed only when the problem says so.

Sommaire

1 Two sequences / 4 pts

(a) For \(11, 16, 21, 26, \dots\) write an explicit formula and find \(a_{25}\). (b) For \(243, 81, 27, \dots\) write an explicit formula and find \(a_6\).

2 Recursive rule / 3 pts

A sequence has \(a_1 = 4\) and \(a_{n+1} = a_n - 3\). (a) List the first four terms. (b) Write an explicit formula. (c) Find \(a_{30}\).

3 Arithmetic series / 4 pts

Consider \(9 + 13 + 17 + \dots\) (a) Find the sum of the first 30 terms. (b) What is the least number of terms whose sum exceeds 1,000?

4 Finite geometric series / 4 pts

No calculator. (a) Find \(7 + 14 + 28 + \dots\) for 9 terms. (b) Evaluate \(\displaystyle\sum_{k=1}^{6} 4\left(\tfrac12\right)^{k-1}\).

5 Infinite series / 3 pts

(a) Find \(18 + 6 + 2 + \dots\) (2 pts). (b) Explain why \(3 + 6 + 12 + \dots\) has no sum.

6 The pendulum / 2 pts

A pendulum’s first swing covers 40 cm (about 15.7 in). Each following swing is 90% as long as the one before. Find the total distance covered before it stops.