Problem Solving

Solution:
An arithmetic progression is of the type a, a+d, a+2d,.... And so on.
Here a is the first term and d is the common difference.
So the 4th term is a+3d and the 12th term is a+11d.
Or 2a+14d = 8.
Sum of first 15 terms is (15/2)*(2a+14d) = 15/2 * 8 = 60.
The correct answer is A.

vavilaladivya wrote:If the sum of the 4th term and the 12th term of an arithmetic progression is 8, what is the sum of the first 15 terms of the progression?

A. 60

B. 120

C. 160

D. 240

E. 84

An arithmetic progression (sequence) is characterized by having each term separated from the next term by a common difference. We can let d = the common difference (i.e., the difference between each pair of consecutive terms) and let the first term = a.

Thus, the first term is a, second term is a + d, and third term is a +2d, so the 4th term is a + 3d and the 12th term is a + 11d. Thus:

(a + 3d) + (a + 11d) = 8

2a + 14d = 8

a + 7d = 4

We are asked to find the sum of the first 15 terms. Since this is an arithmetic progression, we can use the formula sum = quantity x average. The 'quantity' is 15 since there are 15 terms. The 'average' of a finite arithmetic progression is also the median, which in this case is the 8th term. The 8th term in terms of a and d is a + 7d, and we have found that to be 4. Thus:

Sum = 15 x 4 = 60

Answer: A