The question in the image asks:

"Tentukan jumlah 11 suku pertama dari deret aritmetika 14 + 10 + 6 + ..."

This translates to:

"Determine the sum of the first 11 terms of the arithmetic sequence 14 + 10 + 6 + ..."

Step-by-step Solution:

This is an arithmetic sequence where:

• The first term $a = 14$,
• The common difference $d = 10 - 14 = -4$.

The sum $S_n$ of the first $n$ terms of an arithmetic sequence is given by the formula:

$S_n = \frac{n}{2} \left( 2a + (n - 1) d \right)$

For this problem:

• $a = 14$,
• $d = -4$,
• $n = 11$.

Substitute these values into the formula:

$S_{11} = \frac{11}{2} \left( 2(14) + (11 - 1)(-4) \right)$

First, simplify inside the parentheses:

$S_{11} = \frac{11}{2} \left( 28 + 10(-4) \right)$ $S_{11} = \frac{11}{2} \left( 28 - 40 \right)$ $S_{11} = \frac{11}{2} \times (-12)$ $S_{11} = 11 \times (-6)$ $S_{11} = -66$

Conclusion:

The sum of the first 11 terms of the arithmetic sequence is -66.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you find the nth term of an arithmetic sequence?
2. What happens to the sum if the common difference is positive instead of negative?
3. Can you solve for the sum of 20 terms in the same arithmetic sequence?
4. How can you determine if a sequence is arithmetic just by looking at it?
5. What is the relationship between the common difference and the sum of terms?

Tip: When calculating the sum of an arithmetic sequence, always double-check the sign of the common difference—it impacts whether the sequence is increasing or decreasing!