👤
Answered

an auditorium has 54 seats in the first row, 58 seats in the second row and 62 seats in the third row, and so on. Find the general term of this arithmetic sequence

Sagot :

KAntoineDoixgo

✒️SEQUENCES

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

[tex] \large\underline{\mathbb{ANSWER}:} [/tex]

[tex] \qquad \Large \:\: \rm a_n = 4n + 50 [/tex]

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]

First, determine the common difference of the arithmetic sequence.

  • [tex] d = a_2 - a_1 = 58 - 54 = 4 [/tex]
  • [tex] d = a_3 - a_2 = 62 - 58 = 4 [/tex]

The common difference is 4. Substitute it along with the first term to the arithmetic sequence formula.

[tex] \begin{align} & \bold{Formula:} \\ & \quad \boxed{\rm a_n = a_1 + d(n - 1)} \end{align} [/tex]

  • [tex] a_n = 54 + 4(n - 1) [/tex]

  • [tex] a_n = 54 + 4n - 4 [/tex]

  • [tex] a_n = 50 + 4n [/tex]

  • [tex] a_n = 4n + 50 [/tex]

Therefore, the general form of the given arithmetic sequence is an = 4n + 50

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

(ノ^_^)ノ

Go Training: Other Questions