Subjects algebra

Arithmetic Sequence Ed6919

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1. **State the problem:** We have an arithmetic sequence starting at 16 and increasing by 8 each time: 16, 24, 32, 40, ... We want to find the 20ᵗʰ term of this sequence. 2. **Formula for the nᵗʰ term of an arithmetic sequence:** $$a_n = a_1 + (n-1)d$$ where $a_n$ is the nᵗʰ term, $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number. 3. **Identify values:** - $a_1 = 16$ - $d = 8$ - $n = 20$ 4. **Substitute values into the formula:** $$a_{20} = 16 + (20-1) \times 8$$ 5. **Simplify inside the parentheses:** $$a_{20} = 16 + 19 \times 8$$ 6. **Multiply:** $$a_{20} = 16 + 152$$ 7. **Add:** $$a_{20} = 168$$ **Final answer:** The 20ᵗʰ term of the sequence is $168$.