Sequences and Series — Flashcards
ICSE · Class 11 · Mathematics
35 flashcards for Sequences and Series (ICSE Class 11 Mathematics) to test yourself on key terms and facts. Part of the ICSE Class 11 Mathematics syllabus.
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A sequence has nth term a_n = n^2. Write the first four terms and the corresponding ordered list.
Answer
Step 1: Put n = 1, 2, 3, 4. Step 2: a_1 = 1^2 = 1 Step 3: a_2 = 2^2 = 4 Step 4: a_3 = 3^2 = 9 Step 5: a_4 = 4^2 = 16 Answer: The sequence is 1, 4, 9, 16, ...
Show that the sequence 2, 4, 6, 8, ... is a progression and find its nth term.
Answer
Step 1: Check whether an explicit formula exists. Step 2: The terms are even natural numbers. Step 3: The nth term is a_n = 2n. Answer: It is a progression because the terms can be written by an expli…
Why is 2, 3, 5, 7, 11, ... a sequence but not a progression?
Answer
A progression needs an explicit formula for the nth term. The prime-number sequence is an ordered list, so it is a sequence. A known explicit formula for the nth prime number is not available here, so…
Write the first five terms of the sequence with nth term a_n = (n - 3)/4.
Answer
Step 1: Substitute n = 1, 2, 3, 4, 5. Step 2: a_1 = (1 - 3)/4 = -1/2 Step 3: a_2 = (2 - 3)/4 = -1/4 Step 4: a_3 = (3 - 3)/4 = 0 Step 5: a_4 = (4 - 3)/4 = 1/4 Step 6: a_5 = (5 - 3)/4 = 1/2 Answer: -1/2…
Find the 20th term of the sequence a_n = (n - 1)(2 - n)(3 + n).
Answer
Step 1: Put n = 20. Step 2: a_20 = (20 - 1)(2 - 20)(3 + 20) Step 3: a_20 = 19 × (-18) × 23 Step 4: 19 × 18 = 342, and 342 × 23 = 7866 Step 5: Sign is negative. Answer: a_20 = -7866…
A sequence starts with a_1 = 1 and a_n = a_(n-1) + 2 for n >= 2. Find the first five terms.
Answer
Step 1: a_1 = 1 Step 2: a_2 = a_1 + 2 = 3 Step 3: a_3 = a_2 + 2 = 5 Step 4: a_4 = 7 Step 5: a_5 = 9 Answer: 1, 3, 5, 7, 9…
What is the recursive rule of the Fibonacci sequence?
Answer
The sequence starts with a_1 = 1 and a_2 = 1. For n >= 3, a_n = a_(n-1) + a_(n-2). Example: 1, 1, 2, 3, 5, 8, ...
Find the first six terms of the Fibonacci sequence.
Answer
Step 1: a_1 = 1, a_2 = 1 Step 2: a_3 = 1 + 1 = 2 Step 3: a_4 = 2 + 1 = 3 Step 4: a_5 = 3 + 2 = 5 Step 5: a_6 = 5 + 3 = 8 Answer: 1, 1, 2, 3, 5, 8…
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