Write the first five terms of the sequence whose n^ th term is a …

Question

Write the first five terms of the sequence whose $n^{th}$ term is $a _ { n } = ( - 1 ) ^ { n - 1 } \cdot 5 ^ { n + 1 }$

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Answer

Given: $a _ { n } = ( - 1 ) ^ { n - 1 } \cdot 5 ^ { n + 1 }$Putting n = 1, 2, 3, 4 and 5, we get,
$a _ { 1 } = ( - 1 ) ^ { 1 - 1 } \cdot 5 ^ { 1 + 1 } = ( - 1 ) ^ { 0 } \cdot 5 ^ { 2 } = 1 \times 25 = 25$
$a _ { 2 } = ( - 1 ) ^ { 2 - 1 } 5 ^ { 2 + 1 } = ( - 1 ) ^ { 1 } \cdot 5 ^ { 3 } = - 1 \times 125 = - 125$
$a _ { 3 } = ( - 1 ) ^ { 3 - 1 } \cdot 5 ^ { 3 + 1 } = ( - 1 ) ^ { 2 } \cdot 5 ^ { 4 } = 1 \times 625 = 625$
$a _ { 4 } = ( - 1 ) ^ { 4 - 1 } \cdot 5 ^ { 4 + 1 } = ( - 1 ) ^ { 3 } \cdot 5 ^ { 5 } = - 1 \times 3125 = - 3125$
$a _ { 5 } = ( - 1 ) ^ { 5 - 1 } \cdot 5 ^ { 5 + 1 } = ( - 1 ) ^ { 4 } \cdot 5 ^ { 6 } = 1 \times 15625 = 15625$
Therefore, the first five terms are 25, -125, 625, -3125 and 15625.

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