Question

If the third term of an arithmetic progression (AP) is 7, and its 7th term is 2 more than three times its 3rd term, then the sum of its first 20 terms is:

(a) 350

(b) 400

(c) 450

(d) 500

Answer 1

To find the sum of the first 20 terms of the arithmetic progression, we can use the formula for the sum of an arithmetic progression. By solving the given equations, we find that the first term is 1 and the common difference is 2. Substituting these values into the formula, we find that the sum is 1560.

Step-by-step explanation:

To find the sum of the first 20 terms of the arithmetic progression, we need to find the first term and the common difference.

Given that the 3rd term is 7, we can write the equation:

a + 2d = 7 ...(1)

Also, the 7th term is 2 more than three times the 3rd term:

a + 6d = 3(7) + 2 = 23 ...(2)

Solving equations (1) and (2), we get a = 1 and d = 2.

Now, we can use the formula for the sum of an arithmetic progression:

Sum = (n/2)(2a + (n-1)d)

Substituting the values, we get:

Sum = (20/2)(2(1) + (20-1)(2)) = 20(2 + 19(2)) = 20(40 + 38) = 20(78) = 1560

Therefore, the sum of the first 20 terms is 1560.