Arithmetic Sequences

Answer

An arithmetic sequence is a sequence where we add the same number repeatedly to get from one term to the next. Definition: A sequence starting with a number and proceeding by adding one fixed number …

Answer

The common difference (d) is the fixed number added to get from any term to the next term. How to find it: Common difference = Any term - Previous term d = a₂ - a₁ = a₃ - a₂ = a₄ - a₃, etc. Example:…

Answer

Step 1: Check if the difference between consecutive terms is constant 7 - 3 = 4 11 - 7 = 4 15 - 11 = 4 19 - 15 = 4 Step 2: Since all differences are equal to 4, this IS an arithmetic sequence. Comm…

Answer

Step 1: Check differences between consecutive terms 4 - 2 = 2 8 - 4 = 4 16 - 8 = 8 32 - 16 = 16 Step 2: Since the differences (2, 4, 8, 16) are NOT equal, this is NOT an arithmetic sequence. This i…

Answer

Step 1: Identify given information 3rd term (a₃) = 17 7th term (a₇) = 33 Step 2: Find common difference From 3rd to 7th term: position increases by 7-3 = 4 Term increases by 33-17 = 16 So 4d = 16 d =…

Answer

Formula: aₙ = a₁ + (n-1)d Where: • aₙ = nth term • a₁ = first term • n = position of term • d = common difference Why this works: To reach the nth term from the first term, we add the common differe…

Answer

Step 1: Identify the components First term (a₁) = 4 Common difference (d) = 9 - 4 = 5 Required term: n = 15 Step 2: Apply the formula aₙ = a₁ + (n-1)d a₁₅ = 4 + (15-1) × 5 a₁₅ = 4 + 14 × 5 a₁₅ = 4 + …

Answer

Step 1: Write what we know a₅ = 23, a₁₂ = 51 Step 2: Find common difference From 5th to 12th term: position change = 12 - 5 = 7 Term change = 51 - 23 = 28 So 7d = 28 d = 28 ÷ 7 = 4 Step 3: Find firs…