Did you know?
Did you know that an arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant? In this case, the second term is given as 8, and the common difference can be found by subtracting the first term, which is 10, from the second term. By subtracting 10 from 8, we find that the common difference is -2.
Now, using sigma notation, we can write down the sum of the first 50 terms of this arithmetic sequence. The sum is denoted by the Greek letter sigma (∑), with the index variable (k) representing the position of each term in the sequence. In this case, the index variable k ranges from 1 to 50 because we want to sum the first 50 terms.
Therefore, the sum of the 50 terms can be written as ∑(k = 1 to 50) of (8 + (-2)(k-1)). This formula represents adding up each term in the sequence, starting with the second term (k-1), and multiplying the common difference (-2) by the number of terms we have progressed through in the sequence.
