Question

In an AP of 50 terms, the sum of the first 10 terms is 210, and the sum of its last 15 terms is 2565. Find the AP.

A. an​=55+5n
B. an​=15+5n
C. an​=10+5n
D. an​=20+5n

Answer 1

To find the AP, use the formulas for the sum of an AP. Solve the equations to find a = 15 and d = 5. The AP is given by an = 15 + 5n.

Step-by-step explanation:

To find the arithmetic progression (AP), you need to first find the common difference (d). The sum of the first 10 terms is given as 210, so you can use the formula for the sum of an arithmetic series:

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

Substituting the values, you get:

210 = (10/2)(2a + 9d)

The sum of the last 15 terms is given as 2565, so you can again use the formula for sum of an arithmetic series:

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

Substituting the values, you get:

2565 = (15/2)(2a + 14d)

Solving the above two equations, you find that a = 15 and d = 5.

Therefore, the arithmetic progression is given by the formula an = 15 + 5n, which corresponds to option D.