Question Write an explicit formula for $$ a_{n} $$, the $$ n^{ ext {th }} $$ term of the sequence $$ 25,20,15, \ldots $$ Answer Attempt 1 out of 3 $$ a_{n}=\square $$

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Question Write an explicit formula for $$ a_{n} $$, the $$ n^{	ext {th }} $$ term of the sequence $$ 25,20,15, \ldots $$ Answer Attempt 1 out of 3 $$ a_{n}=\square $$

UpStudy AI · Accepted Answer

1. We are given the sequence $$ 25, 20, 15, \ldots $$.
2. This is an arithmetic sequence. The first term is $$ a_1 = 25 $$.
3. The common difference is calculated as:
   $$
   d = 20 - 25 = -5
   $$
4. The explicit formula for the $$ n^{\text{th}} $$ term of an arithmetic sequence is:
   $$
   a_n = a_1 + (n-1)d
   $$
5. Substituting the known values, we have:
   $$
   a_n = 25 + (n-1)(-5)
   $$
6. Simplify the expression:
   $$
   a_n = 25 - 5(n-1) = 25 - 5n + 5 = 30 - 5n
   $$

The explicit formula for the $$ n^{\text{th}} $$ term is:
$$
a_n = 30 - 5n
$$
The explicit formula for the $$ n^{\text{th}} $$ term is $$ a_n = 30 - 5n $$.

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Write an explicit formula for , the term of the sequence
Answer Attempt 1 out of 3

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Question Write an explicit formula for , the term of the sequence Answer Attempt 1 out of 3