Find the common difference of the arithmetic sequence with the n th term $a _ { n } = 5 - 6 n$ .

A) -5
B) -6
C) 6
D) -1
E) 5

Question

Find the common difference of the arithmetic sequence with the n th term   a n = 5 − 6 n a _ { n } = 5 - 6 n a n ​ = 5 − 6 n  .A)  -5B)  -6C)  6D)  -1E)  5

shreyash Srivastava · Accepted Answer

Final Answer : B, Explanation :   In an arithmetic sequence, the common difference is the difference between two consecutive terms. To find the common difference, we can subtract any two consecutive terms. Let's subtract the (n-1)th term from the nth term: a n − a n − 1 = ( 5 − 6 n ) − [ 5 − 6 ( n − 1 ) ] = − 6  a_n - a_{n-1} = (5-6n) - \left[5-6(n-1)\right] = -6  a n ​ − a n − 1 ​ = ( 5 − 6 n ) − [ 5 − 6 ( n − 1 ) ] = − 6 Therefore, the common difference is -6, which is choice B.

Find the common difference of the arithmetic sequence with the n th term $a _ { n } = 5 - 6 n$ .

A) -5
B) -6
C) 6
D) -1
E) 5

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Learning Objectives

Learning Objectives

Related questions

Find the common difference of the arithmetic sequence with the n th term an=5−6na _ { n } = 5 - 6 nan​=5−6n .A) -5B) -6C) 6D) -1E) 5

Definitions

Learning Objectives

Learning Objectives

Related questions

Find the common difference of the arithmetic sequence with the n th term $a _ { n } = 5 - 6 n$ .

A) -5
B) -6
C) 6
D) -1
E) 5