Progressions — Telangana (SSC) Class 10 Mathematics Solutions (Free)

Step 1: Identify first term a = 2 Step 2: Find common difference d = 5 - 2 = 3 Step 3: Use formula aₙ = a + (n-1)d Step 4: a₁₀ = 2 + (10-1) × 3 Step 5: a₁₀ = 2 + 9 × 3 = 2 + 27 = 29 Final Answer: The 10th term is 29

Step 1: First term a = 5, common difference d = 3, n = 20 Step 2: Use formula Sₙ = n/2 × [2a + (n-1)d] Step 3: S₂₀ = 20/2 × [2(5) + (20-1)(3)] Step 4: S₂₀ = 10 × [10 + 19 × 3] Step 5: S₂₀ = 10 × [10 + 57] = 10 × 67 = 670 Final Answer: Sum of first 20 terms = 670

Step 1: Identify first term a = 3 Step 2: Find common ratio r = 6/3 = 2 Step 3: Use formula aₙ = a × r^(n-1) Step 4: a₆ = 3 × 2^(6-1) = 3 × 2⁵ Step 5: a₆ = 3 × 32 = 96 Final Answer: The 6th term is 96

Step 1: First term a = 2, common ratio r = 2, n = 8 Step 2: Use formula Sₙ = a(rⁿ - 1)/(r - 1) Step 3: S₈ = 2(2⁸ - 1)/(2 - 1) Step 4: S₈ = 2(256 - 1)/1 = 2 × 255 Step 5: S₈ = 510 Final Answer: Sum of 8 terms = 510

Step 1: Let first term = a, common difference = d Step 2: a₄ = a + 3d = 13 ... (1) Step 3: a₉ = a + 8d = 33 ... (2) Step 4: Subtract (1) from (2): 5d = 20, so d = 4 Step 5: From (1): a + 3(4) = 13, so a = 1 Step 6: AP is 1, 5, 9, 13, 17, ... Final Answer: AP = 1, 5, 9, 13, ... with a = 1 and d = 4