Find the 27 th term of this
arithmetic sequence.

Hint:

Ask by Stuart Hart. in the United States

Mar 28,2025

Question

Find the 27 th term of this arithmetic sequence. $$ -21,-14,-7,0,7, \ldots $$ $$ a_{27}=[?] $$ Hint: $$ a_{n}=a_{1}+(n-1) d $$

UpStudy AI · Accepted Answer

1. The formula for the $$n$$th term of an arithmetic sequence is given by:
   $$
   a_n = a_1 + (n-1)d
   $$

2. Here, the first term is $$a_1 = -21$$, and the common difference $$d$$ is:
   $$
   d = (-14) - (-21) = 7
   $$

3. To find the 27th term $$a_{27}$$, substitute $$a_1 = -21$$, $$d = 7$$, and $$n = 27$$ into the formula:
   $$
   a_{27} = -21 + (27-1)\times 7
   $$

4. Simplify the expression:
   $$
   a_{27} = -21 + 26 \times 7
   $$
   $$
   a_{27} = -21 + 182
   $$

5. Finally, compute the sum:
   $$
   a_{27} = 161
   $$
The 27th term of the sequence is 161.

Find the 27 th term of this
arithmetic sequence.

Hint:

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