Given the series : 2,5,8,11....What is the type of progression?     Blank 1 Question 18What is the sum from 1st to 5th element?

The given series is an arithmetic progression. This is because the difference between consecutive terms is constant. In this case, the common difference is 3 (5-2 = 3, 8-5 = 3, 11-8 = 3).

The sum of the first n terms of an arithmetic series can be found using the formula: S_n = n/2 * (a + l) where n is the number of terms, a is the first term, and l is the last term.

In this case, we want to find the sum of the first 5 terms. The first term (a) is 2 and the fifth term (which is also the last term in this case, l) can be found using the formula of nth term of an arithmetic progression, which is a + (n-1)*d, where a is the first term, n is the term number and d is the common difference. Here, a = 2, n = 5 and d = 3. So, the fifth term l = 2 + (5-1)*3 = 14.

Substituting these values into the sum formula gives: S_5 = 5/2 * (2 + 14) = 40. So, the sum of the first 5 terms of the series is 40.