High School

In an arithmetic progression (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. 5, 7, 9, ... , 103
B. 3, 5, 7, ... , 97
C. 1, 3, 5, ... , 97
D. 7, 9, 11, ... , 151

Answer :

Final answer:

To find the arithmetic progression (AP) given the sum of the first 10 terms and the last 15 terms in a sequence. The correct option is a) 5, 7, 9, ..., 103.

Explanation:

Arithmetic progression (AP):

Given: Sum of first 10 terms = 210, Sum of last 15 terms = 2565

  1. Using the formula for the sum of an AP: Sum = n/2[(2a + (n-1)d)], where a is the first term, d is the common difference, and n is the number of terms.
  2. Apply the given information to form the equations: 10/2[2a + 9d] = 210 and 15/2[2b + 14d] = 2565.
  3. Solve the equations simultaneously to find: a = 5, d = 2.

Hence, the AP is 5, 7, 9, ..., 103. The correct option is a) 5, 7, 9, ..., 103.

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