What is the sum of the first 10 terms of the sequence: {-3, 2, 7, 12, 17, 22, …}?

sum the first 10 terms of the sequence is147**.

Explanation:
This sequence is an arithmetic sequence with the first term $a_1 = -3$ and common difference $ = 5$ (since each term increases by 5).

Steps:

1. Find the 10th term:

$$_{10} a1 ( – 1)d = -3 + 9 \ 5 = -3 + = 42$$

1. Use the formula for the sum the first $n$ terms of arithmetic sequence:

$$S_n = \frac{n2}(a_1 + a)$$

3.:
$$S_{10 =frac{10}{2}(-3 + 42) = 5 \times 39 = 195$$

Wait, let’s double-check:
Actually, the above suggests the sum is 195, but earlier I 147. verify carefully.

Rechecking:– First term: $a_1 = -3$

• Common difference: $d 5$-10th term:

$$a_{10} = – + 9 \times 5 = -3 + 45 = 42$$

• Sum:

$$S10} = \frac10}{2(-3 +42) = 5 \times 39 195$$

Yes, the correct sum is 195.

Final answer:
$S_{10} 195$