Question 1160078
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These are straightforward problems involving arithmetic and geometric sequences; you can do the arithmetic....<br>
1. Find the 25th term of the arithmetic sequence  ‒7, ‒4, ‒1, 2, ...<br>
The common difference is +3
The 25th term is the first term, plus the common difference 24 times<br>
2. In an arithmetic sequence, if a4 = 18 and a10 = 30, determine a1, d, and an.
Then write the first four terms of the sequence.<br>
The difference between the 4th term and the 10th term is 30-18 = 12; that difference is 6 times the common difference.
So you can easily find the common difference, d.
Then the first term a1 is the 4th term, minus 3 times the common difference.
Then the formula for an is the first term, plus (n-1) times the common difference.<br>
3. In a geometric sequence, if a3 = ‒5 and a6 = 40, determine a1, r, and an.
Then write the first three terms of the sequence.<br>
The 6th term, 40, is the 3rd term, (-5), multiplied by the common ratio 3 times:
{{{40 = (-5)(r^3)}}}
{{{r^3 = -8}}}
{{{r = -2}}}<br>
You have r; the first term a1 is the third term, -5, DIVIDED BY the common ratio two times; the formula for an is the first term, multiplied by the common ratio (n-1) times.<br>