A Statement $$\mathrm { S } _ { \mathrm { n } }$$

question 205

Essay

A statement
$$\mathrm { S } _ { \mathrm { n } }$$ about the positive integers is given. Write statements
$\mathrm { S } _ { 1 } , \mathrm {~S} _ { 2 }$ and S
$\mathrm { S } _ { 3 }$ , and show that each of these
statements is true.
- $$S _ { n } : 2 + 7 + 12 + \ldots + ( 5 n - 3 ) = \frac { n ( 5 n - 1 ) } { 2 }$$

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Definitions:

Corms

Short, vertical, swollen underground plant stems that serve as storage organs to survive winter or dry months and to propagate new plants.

Germination

The process by which a plant grows from a seed or similar structure.

Imbibition

The process of absorption of water by plant tissues or seeds, often leading to swelling, which is critical for seed germination and plant growth.

Anaerobic Soils

Soils that lack oxygen, often found in waterlogged conditions, affecting the types of organisms and chemical reactions that can occur.