Question

Write the first five terms of the sequences whose n^th term is:

`a_n = (-1)^(n-1) 5^(n+1)`

Answer 1

a_n = (−1)ⁿ⁻¹ 5ⁿ⁺¹  

Substituting n = 1, 2, 3, 4, 5, we get

a₁ = (-1)^{1 - 1} 5^{1 + 1} = (−1)⁰ 5² = 25,

a₂ = (-1)^{2 - 1} 5^{2 + 1} = (−1)¹ 5³ = −125,

a₃ = (-1)^{3 - 1} 5^{3 + 1} = (−1)² 5⁴ = 625,

a₄ = (-1)^{4 - 1} 5^{4 + 1} = (−1)³ 5⁵ = −3125,

a₅ = (-1)^{5 - 1} 5^{5 + 1} = (−1)⁴ 5⁶ = 15625

The first five terms are 25, −125, 625, −3125, 15625.