If the 4th term of an AP is 17 and the 10th term is 41, find the 15th term. Answer: 61

Answer: 61

Step-by-step solution

Step 1: Set up equations using the nth term formula

We know that the $n^{\text{th}}$ term of an Arithmetic Progression is given by $a_n = a + (n - 1)d$ , where $a$ is the first term and $d$ is the common difference. For the 4th term, $n = 4$ , which gives $a + 3d = 17$ . For the 10th term, $n = 10$ , which gives $a + 9d = 41$ .

Step 2: Solve for the common difference d

Subtracting equation (1) from equation (2) eliminates the variable $a$ . This leaves $6d = 24$ , which simplifies to $d = 4$ .

Step 3: Solve for the first term a

Substitute the value $d = 4$ back into equation (1). We get $a + 12 = 17$ , which gives $a = 5$ .

Step 4: Calculate the 15th term

To find the 15th term, substitute $a = 5$ , $n = 15$ , and $d = 4$ into $a_n = a + (n - 1)d$ . Multiplying $14$ by $4$ gives $56$ , and adding $5$ gives $61$ .

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