Given: The sum to $$ n $$ terms of an arithmetic sequence is $$ S_{n}=3 n^{2}-5 n $$. 1.1.1 $$ \quad $$ Calculate the sum of the first 21 terms of this sequence.

Question

UpStudy AI · Accepted Answer

**Step 1. Express the formula for the sum of the first $$ n $$ terms**

The sum to $$ n $$ terms of the arithmetic sequence is given by
$$
S_n = 3n^2 - 5n.
$$

**Step 2. Substitute $$ n = 21 $$ into the formula**

We need to calculate the sum of the first 21 terms:
$$
S_{21} = 3(21)^2 - 5(21).
$$

**Step 3. Calculate $$ 21^2 $$ and multiply by 3**

First, compute:
$$
21^2 = 441.
$$
Then multiply by 3:
$$
3 \times 441 = 1323.
$$

**Step 4. Multiply 21 by 5**

Multiply:
$$
5 \times 21 = 105.
$$

**Step 5. Subtract the product from the result in Step 3**

Subtract:
$$
S_{21} = 1323 - 105.
$$

**Step 6. Final calculation**

$$
S_{21} = 1218.
$$

Thus, the sum of the first 21 terms is $$\boxed{1218}$$.
The sum of the first 21 terms is 1218.

Given: The sum to terms of an arithmetic sequence is .
1.1.1 Calculate the sum of the first 21 terms of this sequence.

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Arithmetic Questions

Given: The sum to terms of an arithmetic sequence is . 1.1.1 Calculate the sum of the first 21 terms of this sequence.