This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Let 'a' be the first term and 'l' be the last term for both Arithmetic Progressions (APs). The formula for the last term of an AP is: l = a + (n - 1)d where 'n' is the number of terms and 'd' is the common difference. Step 1: Write the expression for the last term of the first AP. Given: n₁ = 21, d₁ = 9 l = a + (n₁ - 1)d₁ l = a + (21 - 1)9 l = a + (20)9 l = a + 180 Step 2: Write the expression for the last term of the second AP. Given: d₂ = 4, n₂ = ? l = a + (n₂ - 1)d₂ l = a + (n₂ - 1)4 Step 3: Equate the expressions for 'l' since the last terms are the same. a + 180 = a + (n₂ - 1)4 Step 4: Solve for n₂. Subtract 'a' from both sides: 180 = (n₂ - 1)4 Divide both sides by 4: 180 / 4 = n₂ - 1 45 = n₂ - 1 Add 1 to both sides: n₂ = 45 + 1 n₂ = 46 The other AP has 46 terms. Send me the next one 📸