Question

alg : cc unit 1 lt1 30 given: 306, 302, 298, 294, 290, ... what is the common difference for this arithmetic sequence? d = write the simplified explicit formula (expression) for the given arithmetic sequence. a_n = find the 6th term of this arithmetic sequence. a_15 =

Explanation:

Step1: Find common difference \( d \)

In an arithmetic sequence, \( d = a_{n + 1}-a_n \). Take \( a_1 = 306 \), \( a_2 = 302 \). So \( d=302 - 306=-4 \).

Step2: Find explicit formula \( a_n \)

The explicit formula for an arithmetic sequence is \( a_n=a_1+(n - 1)d \). Substitute \( a_1 = 306 \), \( d=-4 \):
\( a_n=306+(n - 1)(-4)=306-4n + 4=310-4n \).

Step3: Find the 6th term \( a_6 \)

Substitute \( n = 6 \) into \( a_n=310-4n \):
\( a_6=310-4\times6=310 - 24 = 286 \).

Step4: Find the 15th term \( a_{15} \)

Substitute \( n = 15 \) into \( a_n=310-4n \):
\( a_{15}=310-4\times15=310 - 60 = 250 \).

Answer:

s:

• Common difference \( d=-4 \)
• Explicit formula \( a_n = 310 - 4n \)
• 6th term \( a_6 = 286 \)
• 15th term \( a_{15}=250 \)