Use the Formula for the General Term of an Arithmetic Sequence
Choose the one alternative that best completes the statement or answers the question.
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the
sequence with the given first term, a1, and common difference, d.
-Find a 19 when $a _ { 1 } = - 4 , d = - \frac { 5 } { 3 }$.
A) $- 34$
B) $- \frac { 107 } { 3 }$
C) 26
D) $\frac { 83 } { 3 }$

Question

Quizplus · Accepted Answer

The formula for the nth term of an arithmetic sequence is:$$a_n = a_1 + (n-1)d$$where $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number.Substituting the given values into the formula, we get:$$a_{19} = -4 + (19-1)\left(-\frac{5}{3}\right)$$$$a_{19} = -4 + (18)\left(-\frac{5}{3}\right)$$$$a_{19} = -4 - 30$$$$a_{19} = -34$$Therefore, the 19th term of the sequence is -34.

Use the Formula for the General Term of an Arithmetic a1=−4,d=−53a _ { 1 } = - 4 , d = - \frac { 5 } { 3 }a1​=−4,d=−35​

Use the Formula for the General Term of an Arithmetic $a _ { 1 } = - 4 , d = - \frac { 5 } { 3 }$