An arithmetic sequence is given by 𝑢𝑛=3𝑛−7.Find ∑𝑖=719𝑢𝑖.

The given arithmetic sequence is un = 3n - 7.

We need to find the sum of terms from u7 to u19.

First, let's find the 7th term (u7) and the 19th term (u19) of the sequence:

u7 = 37 - 7 = 14 u19 = 319 - 7 = 50

The sum of an arithmetic sequence can be found using the formula:

S = n/2 * (a + l)

where: n is the number of terms, a is the first term, and l is the last term.

Here, n = 19 - 7 + 1 = 13 (we add 1 because both 7th and 19th terms are inclusive), a = u7 = 14, and l = u19 = 50.

Substituting these values into the formula, we get:

S = 13/2 * (14 + 50) = 6.5 * 64 = 416

So, the sum of the terms from u7 to u19 of the given arithmetic sequence is 416.