<ol> <li> <p>Find the 15th term of the AP: §§V0(5,500,4)§§, §§(§§V0(5,500,4)§§ + 4)§§, §§(§§V0(5,500,4)§§ + 8)§§, §§(§§V0(5,500,4)§§ + 12)§§ ...</p> </li> <li> <p>The first term of an AP is §§V1(8,10,1)§§, and the common difference is -3. Find the 10th term.</p> </li> <li> <p>In an AP, the 6th term is §§V2(15,25,1)§§ and the 14th term is §§(§§V2(15,25,1)§§ + 8 * §§V3(3,6,1)§§)§§. Find the common difference.</p> </li> <li> <p>The sum of the first §§V0(10,15,1)§§ terms of an AP is §§V1(300,400,10)§§. If the first term is §§V2(3,7,1)§§, find the common difference.</p> </li> <li> <p>How many terms of the AP §§V3(4,10,1)§§, §§(§§V3(4,10,1)§§ + 3)§§, §§(§§V3(4,10,1)§§ + 6)§§, ... sum to §§V4(200,350,10)§§?</p> </li> <li> <p>In an AP, the §§V5(3,5,1)§§rd term is §§V6(10,15,1)§§ and the §§V7(8,10,1)§§th term is §§V8(25,35,1)§§. Find the §§V9(15,25,1)§§th term.</p> </li> <li> <p>The angles of a triangle form an AP. The smallest angle is §§V10(30,45,5)§§°. Find the other angles.</p> </li> <li> <p>Find the sum of all integers between §§V11(50,100,10)§§ and §§V12(150,250,10)§§ divisible by §§V13(5,7,1)§§.</p> </li> <li> <p>In an AP, S_n = §§V14(2,5,1)§§n² + §§V15(1,5,1)§§n. Find the first term and common difference.</p> </li> <li> <p>In an AP, the §§V0(4,6,1)§§th term is zero. Prove that the §§V1(20,30,5)§§th term is triple the §§V2(10,15,1)§§th term.</p> </li> <li> <p>Three numbers in AP sum to §§V3(20,30,2)§§. Their product is §§V4(400,600,20)§§. Find the numbers.</p> </li> <li> <p>If §§V5(10,20,2)§§, §§V6(15,25,2)§§, §§V7(20,30,2)§§ are in AP, show that 2ק§V6(15,25,2)§§ = §§V5(10,20,2)§§ + §§V7(20,30,2)§§.</p> </li> <li> <p>The sum of the first n terms of an AP is §§V8(2,5,1)§§n² + §§V9(5,10,1)§§n. Find the §§V10(8,12,1)§§th term.</p> </li> <li> <p>In an AP, S_{§§V11(5,15,1)§§} = S_{§§V12(10,20,1)§§} (§§V11(5,15,1)§§≠§§V12(10,20,1)§§). Prove S_{§§V11(5,15,1)§§+§§V12(10,20,1)§§} = 0.</p> </li> <li> <p>Find §§V13(1,10,1)§§ so that §§(2ק§V13(1,10,1)§§+1)§§, §§V14(8,12,1)§§, and §§(5ק§V13(1,10,1)§§+2)§§ form an AP.</p> </li> <li> <p>The digits of a three-digit number are in AP. Their sum is §§V15(12,18,1)§§, and reversing the digits decreases the number by §§V16(300,400,10)§§. Find the number.</p> </li> <li> <p>A clock strikes hours (§§V17(1,1,1)§§ to §§V18(12,12,1)§§). Total strikes in a §§V19(1,3,1)§§ day period?</p> </li> <li> <p>Salary increases by $§§V20(400,600,50)§§ annually. After §§V21(8,12,1)§§ years, total earnings are $§§V22(800000,900000,10000)§§. Find the starting salary.</p> </li> <li> <p>In an AP, a_{§§V23(4,6,1)§§} = §§V24(25,35,1)§§ and a_{§§V25(10,15,1)§§} = §§V26(60,70,1)§§. Find a_{§§V27(18,22,1)§§}.</p> </li> <li> <p>Prove that the sum of the first \( n \) terms of an arithmetic progression (AP) is given by: \[ \frac{n}{2} \left[ 2a + (n - 1)d \right] \]</p> </li> <li> <p>Given an arithmetic progression (AP) with first term 𝑎 = 5 and common difference 𝑑 = 3, complete the table below using:</p> <ul> <li> <b>The \(n-th\) term formula:</b> \[ T_n = a + (n-1)d \] </li> <li> <b> The sum of the first \(n\) term formula:</b> \[ S_n = \frac{n}{2} \left[2a + (n+1)d \right] \] </li> </ul> <table class="table table-bordered table-hover text-center"> <thead class="thead-light"> <tr> <th>n</th> <th>\( a_n \)</th> <th>\( S_n \)</th> </tr> </thead> <tbody> <tr> <td>§§V31(1,10,1)§§</td> <td>_____</td> <td>_____</td> </tr> <tr> <td>§§(§§V31(1,10,1)§§ + 1)§§</td> <td>_____</td> <td>_____</td> </tr> <tr> <td>§§(§§V31(1,10,1)§§ + 2)§§</td> <td>_____</td> <td>_____</td> </tr> <tr> <td>§§(§§V31(1,10,1)§§ + 3)§§</td> <td>_____</td> <td>_____</td> </tr> <tr> <td>§§(§§V31(1,10,1)§§ + 4)§§</td> <td>_____</td> <td>_____</td> </tr> </tbody> </table> </li> </ol>