Find a formula for a_n?for the arithmetic sequence. ?a₃ = 94,a₆ = 87 ? A)a_n?= $\frac { 7 } { 3 }$ n - 101 B)a_n?= $- \frac { 7 } { 3 }$ n + 101 C)a_n?= 101 - 303n D)a_n?= $\frac { 7 } { 3 }$ n + 303 E)a_n?= 101 + 303n

Question

Quizplus · Accepted Answer

We can use the formula for the nth term in an arithmetic sequence to find aS1U1B1n:
aS1U1B1n = aS1U1B0 + (n-1)d
where d is the common difference.

Using the given values, we have:
aS1U1B13 = aS1U1B0 + 12d = 94
aS1U1B16 = aS1U1B0 + 15d = 87

Subtracting the first equation from the second, we get:
aS1U1B16 - aS1U1B13 = (aS1U1B0 + 15d) - (aS1U1B0 + 12d) = 3d = -7

Therefore, d = -7/3.

Substituting this value of d into the first equation, we get:
aS1U1B13 = aS1U1B0 + 12(-7/3) = aS1U1B0 - 28

Solving for aS1U1B0, we get:
aS1U1B0 = 94 + 28 = 122

Thus, the formula for aS1U1B1n is:
aS1U1B1n = 122 - (7/3)(n-1)

Simplifying this expression, we get:
aS1U1B1n = (-7/3)n + (7/3)(4) + 122
aS1U1B1n = (-7/3)n + (28/3) + 122
aS1U1B1n = (-7/3)n + (154/3)

Comparing this equation with the options given, we see that choice (B) matches.

Find a Formula for An ?for the Arithmetic Sequence 73\frac { 7 } { 3 }37​

Find a Formula for A_n?for the Arithmetic Sequence $\frac { 7 } { 3 }$