Sequences and Series — Flashcards
NIOS · Class 12 · Mathematics
25 flashcards for Sequences and Series (NIOS Class 12 Mathematics) to test yourself on key terms and facts. Part of the NIOS Class 12 Mathematics syllabus.
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Find the 15th term of the A.P.: 3, 7, 11, 15, ...
Answer
Using formula: tₙ = a + (n-1)d Given: a = 3, d = 7 - 3 = 4, n = 15 Step 1: t₁₅ = 3 + (15-1) × 4 Step 2: t₁₅ = 3 + 14 × 4 Step 3: t₁₅ = 3 + 56 Answer: t₁₅ = 59…
The 10th term of an A.P. is -15 and the 31st term is -57. Find the common difference and first term.
Answer
Using: tₙ = a + (n-1)d Given: t₁₀ = -15, t₃₁ = -57 Step 1: Write two equations a + 9d = -15 ... (1) a + 30d = -57 ... (2) Step 2: Subtract (1) from (2) 21d = -42 d = -2 Step 3: Substitute d in equa…
Which term of the A.P. 5, 11, 17, ... equals 119?
Answer
Using: tₙ = a + (n-1)d Given: a = 5, d = 11 - 5 = 6, tₙ = 119 Step 1: Set up equation 119 = 5 + (n-1) × 6 Step 2: Simplify 119 - 5 = (n-1) × 6 114 = (n-1) × 6 Step 3: Solve for n n - 1 = 114/6 = 19…
Find the sum of the first 20 terms of the A.P.: 2, 5, 8, 11, ...
Answer
Using: Sₙ = n/2 [2a + (n-1)d] Given: a = 2, d = 5 - 2 = 3, n = 20 Step 1: Substitute values S₂₀ = 20/2 [2(2) + (20-1) × 3] Step 2: Simplify inside brackets S₂₀ = 10 [4 + 19 × 3] S₂₀ = 10 [4 + 57] S₂…
An A.P. has first term 10, last term 50, and sum 480. Find the number of terms and common difference.
Answer
Using: Sₙ = n/2 (a + l) and tₙ = a + (n-1)d Given: a = 10, l = tₙ = 50, Sₙ = 480 Step 1: Find n using sum formula 480 = n/2 (10 + 50) 480 = n/2 × 60 480 = 30n n = 16 Step 2: Find d using general ter…
Insert 3 arithmetic means between 2 and 14.
Answer
Need to find 3 A.M.s between 2 and 14, so sequence has 5 terms: 2, A₁, A₂, A₃, 14 Step 1: Use formula for total terms If we have n A.M.s inserted, total terms = n + 2 = 5 Step 2: Find common differe…
Find the A.M. between 16 and 24.
Answer
The arithmetic mean between two numbers a and b is given by: A.M. = (a + b)/2 Given: a = 16, b = 24 Step 1: Apply formula A.M. = (16 + 24)/2 Step 2: Calculate A.M. = 40/2 = 20 Verification: 16, 20…
Find the 8th term of the G.P.: 2, 6, 18, 54, ...
Answer
Using formula: tₙ = arⁿ⁻¹ Given: a = 2, r = 6/2 = 3, n = 8 Step 1: Identify first term and common ratio a = 2, r = 3 Step 2: Apply formula t₈ = 2 × 3⁸⁻¹ t₈ = 2 × 3⁷ Step 3: Calculate 3⁷ 3⁷ = 2187 …
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