A sequence is deﬁned recursively as follows: $$s _ { k } = 5 s _ { k - 1 } + 1$$ for all integers $k \geq 1$
$$s _ { 0 } = 1 \text {. }$$
Use mathematical induction to verify that this sequence satisﬁes the explicit formula $$s _ { n } = \frac { 5 ^ { n + 1 } - 1 } { 4 } \quad \text { for all integers } n \geq 0 \text {. }$$

Question

A sequence is deﬁned recursively as follows: $$s _ { k } = 5 s _ { k - 1 } + 1$$ for all integers $k \geq 1$ 
$$s _ { 0 } = 1 \text {. }$$
Use mathematical induction to verify that this sequence satisﬁes the explicit formula $$s _ { n } = \frac { 5 ^ { n + 1 } - 1 } { 4 } \quad \text { for all integers } n \geq 0 \text {. }$$

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The Answer of A sequence is deﬁned recursively as follows: $$s _ { k } = 5 s _ { k - 1 } + 1$$ for all integers $k \geq 1$ 
$$s _ { 0 } = 1 \text {. }$$
Use mathematical induction to verify that this sequence satisﬁes the explicit formula $$s _ { n } = \frac { 5 ^ { n + 1 } - 1 } { 4 } \quad \text { for all integers } n \geq 0 \text {. }$$

A Sequence Is Deﬁned Recursively as Follows sk=5sk−1+1s _ { k } = 5 s _ { k - 1 } + 1sk​=5sk−1​+1

A Sequence Is Deﬁned Recursively as Follows $s _ { k } = 5 s _ { k - 1 } + 1$