Subjects algebra

Sum First 19

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Sum First 19


1. The problem asks for the sum of the first 19 terms of a sequence, but the sequence type was not specified. Assuming it is an arithmetic sequence. 2. The formula for the sum of the first $n$ terms of an arithmetic sequence is: $$ S_n = \frac{n}{2} (2a_1 + (n - 1)d) $$ where $a_1$ is the first term, $d$ is the common difference, and $n$ is the number of terms. 3. Since the first term and common difference are not given, if we assume the sequence is the natural numbers starting from 1, then $a_1 = 1$ and $d = 1$. 4. Substitute $a_1 = 1$, $d = 1$, and $n = 19$ into the formula: $$ S_{19} = \frac{19}{2} (2 \times 1 + (19 - 1) \times 1) $$ $$ = \frac{19}{2} (2 + 18) = \frac{19}{2} \times 20 = 19 \times 10 = 190 $$ 5. Therefore, the sum of the first 19 natural numbers is $190$.