f the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum offirst n terms.

Let's solve the problem step by step:

Step 1: Find the common difference (d) of the arithmetic progression (AP). To find the common difference, we can subtract the 6th term from the 7th term: 7th term - 6th term = 49 - (6th term)

Step 2: Find the value of the 6th term. To find the value of the 6th term, we can use the formula for the nth term of an AP: 6th term = 7th term - (n-1) * d

Step 3: Find the value of the first term (a). To find the value of the first term, we can use the formula for the nth term of an AP: a = 6th term - (6-1) * d

Step 4: Find the value of the common difference (d) using the 16th term. To find the common difference, we can subtract the 16th term from the 17th term: 17th term - 16th term = 289 - (16th term)

Step 5: Find the value of the 16th term. To find the value of the 16th term, we can use the formula for the nth term of an AP: 16th term = 17th term - (n-1) * d

Step 6: Find the value of the first term (a) using the 16th term. To find the value of the first term, we can use the formula for the nth term of an AP: a = 16th term - (16-1) * d

Step 7: Find the value of the first term (a) using the 6th term. To find the value of the first term, we can use the formula for the nth term of an AP: a = 6th term - (6-1) * d

Step 8: Find the value of the common difference (d) using the first term (a). To find the common difference, we can subtract the 6th term from the 7th term: 7th term - 6th term = 49 - (6th term)

Step 9: Find the value of the first term (a) using the common difference (d). To find the value of the first term, we can use the formula for the nth term of an AP: a = 6th term - (6-1) * d

Step 10: Find the sum of the first n terms of the AP. To find the sum of the first n terms, we can use the formula for the sum of an AP: Sum = (n/2) * (2a + (n-1) * d)

By following these steps, we can find the sum of the first n terms of the given arithmetic progression.