Find the first six terms of the sequence. a₁ = -8, a_n = 5a_{n - 1}

Solution:

Given, first term, a₁ = -8,

a_n = 5a_{n - 1}

We have to find the first six terms of the sequence.

\(\\a_{2}=5\times a_{2-1}\\a_{2}=5\times a_{1}\\a_{2}=5\times (-8)\\a_{2}=-40\)

\(\\a_{3}=5\times a_{3-1}\\a_{3}=5\times a_{2}\\a_{3}=5\times (-40)\\a_{3}=-200\)

\(\\a_{4}=5\times a_{4-1}\\a_{4}=5\times a_{3}\\a_{4}=5\times (-200)\\a_{4}=-1000\)

\(\\a_{5}=5\times a_{5-1}\\a_{5}=5\times a_{4}\\a_{5}=5\times (-1000)\\a_{5}=-5000\)

\(\\a_{6}=5\times a_{6-1}\\a_{6}=5\times a_{5}\\a_{6}=5\times (-5000)\\a_{5}=-25000\)

Therefore, the first six terms are -8, -40, -200, -1000, -5000 and -25000.

Find the first six terms of the sequence. a₁ = -8, a_n = 5a_{n - 1}

Summary:

The first six terms of the sequence when a₁ = -8, a_n = 5a_{n - 1} are -8, -40, -200, -1000, -5000 and -25000.