QuestionAugust 25, 2025

Write a recursive formula for a_(n) , the n^th term of the sequence 2,-7,-16,-25,ldots Answer Attempt 1 out of 2 a_(1)=square a_(n)=square

Write a recursive formula for a_(n) , the n^th term of the sequence 2,-7,-16,-25,ldots Answer Attempt 1 out of 2 a_(1)=square a_(n)=square
Write a recursive formula for a_(n) , the n^th term of the sequence 2,-7,-16,-25,ldots Answer Attempt 1 out of 2 a_(1)=square a_(n)=square

Solution
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Answer

a_1 = 2 ### a_n = a_{n-1} - 9 for n > 1 Explanation 1. Identify the first term The first term of the sequence is a_1 = 2. 2. Determine the common difference Calculate the difference between consecutive terms: -7 - 2 = -9, -16 - (-7) = -9. The common difference is d = -9. 3. Write the recursive formula Use the formula for a recursive sequence: a_n = a_{n-1} + d. Here, d = -9.

Explanation

1. Identify the first term<br /> The first term of the sequence is $a_1 = 2$.<br />2. Determine the common difference<br /> Calculate the difference between consecutive terms: $-7 - 2 = -9$, $-16 - (-7) = -9$. The common difference is $d = -9$.<br />3. Write the recursive formula<br /> Use the formula for a recursive sequence: $a_n = a_{n-1} + d$. Here, $d = -9$.
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