The first and the last term of an arithmetic progression are in the ratio of 3:4. The sum of all terms is 210 and there are 6 terms in total. Commute common difference.

Answer 1

Let's denote the first term as a and the common difference as d.

We can write the first term as a and the last term as a + 5d (since there are 6 terms in total).

Given that the first term is 3/4 times the last term, we have the equation:

a = (3/4)(a + 5d)

Expanding the equation, we get:

4a = 3a + 15d

Simplifying, we have:

a = 15d

Since the sum of all terms is 210, we can express this as:

(6/2)(a + (a + 5d)) = 210

Simplifying further, we have:

3(a + (a + 5d)) = 210

3(2a + 5d) = 210

6a + 15d = 210

Since we know a = 15d from the previous equation, we can substitute this into the equation:

6(15d) + 15d = 210

90d + 15d = 210

105d = 210

Dividing both sides by 105, we get:

d = 2

Therefore, the common difference is 2.