Question

The sum of an arithmetic progression is 220. If the first term is 5 and the last term is 35, find the number of terms in the progression.

a) 9
b) 10
c) 11
d) 12

Answer 1

The number of terms in the arithmetic progression is 1.

Step-by-step explanation:

To find the number of terms in the arithmetic progression, we can use the formula:

n = (last term - first term) / common difference + 1

In this case, the first term is 5, the last term is 35, and the sum of the progression is 220. The common difference can be found by dividing the difference between the first and last term by the number of terms in the progression (n-1). Using the given information, we can calculate:

common difference = (last term - first term) / (n-1) = (35 - 5) / (n-1) = 30 / (n-1)

We can also use the formula for the sum of an arithmetic progression:

sum = (n/2)(first term + last term) = (n/2)(5 + 35) = 20n + 200

Since the sum is given as 220, we can set up the equation:

20n + 200 = 220

Simplifying the equation:

20n = 220 - 200 = 20

n = 20/20 = 1

Therefore, there is only 1 term in the progression.