Write the first five terms of the arithmetic sequence. $a _ { 5 } = 1 , a _ { 15 } = 21$
A)-5, -3, -1, 1, 3
B)-7, -14, -28, -56, -112
C)-7, -9, -11, -13, -15
D)-7, -5, -12, -19, -26
E)-7, -5, -3, -1, 1

Question

Write the first five terms of the arithmetic sequence.   $a _ { 5 } = 1 , a _ { 15 } = 21$  
A)-5, -3, -1, 1, 3
B)-7, -14, -28, -56, -112
C)-7, -9, -11, -13, -15
D)-7, -5, -12, -19, -26
E)-7, -5, -3, -1, 1

Quizplus · Accepted Answer

Given $a_5 = 1$ and $a_{15} = 21$, we find the common difference $d$ and the first term $a_1$. The formula for the $n$th term of an arithmetic sequence is $a_n = a_1 + (n-1)d$. Substituting $n = 5$ and $n = 15$ gives two equations: $1 = a_1 + 4d$ and $21 = a_1 + 14d$. Solving these equations simultaneously yields $d = 2$ and $a_1 = -7$. Thus, the first five terms are -7, -5, -3, -1, 1.

Write the First Five Terms of the Arithmetic Sequence a5=1,a15=21a _ { 5 } = 1 , a _ { 15 } = 21a5​=1,a15​=21

Write the First Five Terms of the Arithmetic Sequence $a _ { 5 } = 1 , a _ { 15 } = 21$