Some Special Sequences — Flashcards
NIOS · Class 12 · Mathematics
25 flashcards for Some Special Sequences (NIOS Class 12 Mathematics) to test yourself on key terms and facts. Sample: "Find the first 6 terms.
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Find the first 6 terms of the sequence where T_n = 2n + 1
Answer
Step 1: Substitute n = 1, 2, 3, 4, 5, 6 into T_n = 2n + 1 Step 2: T_1 = 2(1) + 1 = 3 Step 3: T_2 = 2(2) + 1 = 5 Step 4: T_3 = 2(3) + 1 = 7 Step 5: T_4 = 2(4) + 1 = 9 Step 6: T_5 = 2(5) + 1 = 11 Step 7…
Find the first 6 terms of the sequence where a_n = n² - n + 1
Answer
Step 1: Substitute n = 1, 2, 3, 4, 5, 6 into a_n = n² - n + 1 Step 2: a_1 = (1)² - 1 + 1 = 1 - 1 + 1 = 1 Step 3: a_2 = (2)² - 2 + 1 = 4 - 2 + 1 = 3 Step 4: a_3 = (3)² - 3 + 1 = 9 - 3 + 1 = 7 Step 5: a…
Find the nth term of the series: -2 + 4 - 6 + 8 - ...
Answer
Step 1: Observe the pattern - Terms alternate in sign (negative, positive, negative, positive...) - Absolute values: 2, 4, 6, 8, ... (these are 2n) Step 2: Create the nth term formula - For alternati…
Find the nth term of the series: 4 + 16 + 64 + 256 + ...
Answer
Step 1: Rewrite the series to identify the pattern 4 + 16 + 64 + 256 + ... = 4¹ + 4² + 4³ + 4⁴ + ... Step 2: Verify the pattern - 4¹ = 4 - 4² = 16 - 4³ = 64 - 4⁴ = 256 Step 3: General term Each term…
Formula for sum of first n natural numbers: Σn = ?
Answer
Formula: Σn = n(n + 1)/2 Where: - n = number of natural numbers to sum - The formula gives the sum 1 + 2 + 3 + ... + n Example: Find sum of first 10 natural numbers Step 1: Use Σn = n(n + 1)/2 Step …
Find the sum of first 15 natural numbers using the formula Σn = n(n + 1)/2
Answer
Step 1: Identify what we need Sum of 1 + 2 + 3 + ... + 15 Step 2: Use the formula Σn = n(n + 1)/2 Step 3: Substitute n = 15 Σ15 = 15(15 + 1)/2 = 15(16)/2 = 240/2 = 120 Step 4: Verify…
Formula for sum of squares of first n natural numbers: Σn² = ?
Answer
Formula: Σn² = n(n + 1)(2n + 1)/6 Where: - n = number of terms - This gives 1² + 2² + 3² + ... + n² Example: Find 1² + 2² + 3² + 4² + 5² Step 1: Use Σn² = n(n + 1)(2n + 1)/6 Step 2: Substitute n = 5…
Find 1² + 2² + 3² + 4² + ... + 10² using the formula for sum of squares
Answer
Step 1: Identify what we need Sum of squares from 1 to 10 Step 2: Use the formula Σn² = n(n + 1)(2n + 1)/6 Step 3: Substitute n = 10 Σ10² = 10(10 + 1)(2·10 + 1)/6 = 10(11)(21)/6 = 2310/6…
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