Use the Summation Properties to Evaluate the Series - $$\sum _ { i = 1 } ^ { 4 } \left( 4 i ^ { 2 } + 3 i - 1 \right)$$

question 541

Multiple Choice

Use the summation properties to evaluate the series. The following rules may be needed: $$\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 }$$
- $$\sum _ { i = 1 } ^ { 4 } \left( 4 i ^ { 2 } + 3 i - 1 \right)$$

• A) 146
• B) 149
• C) 154
• D) 126

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Definitions:

Dissolved Gas

Gases that are incorporated into magma and can expand, leading to explosive volcanic eruptions as pressure decreases.

Rhyolite

A mostly fine-grained, felsic igneous rock, generally of volcanic origin; can contain glass, volcanic ash, pieces of pumice, and variable amounts of visible crystals (phenocrysts).

Thermal Energy

The internal energy present in a system due to the random movements of its molecules or atoms.

Conduction

The process by which heat or electricity is directly transmitted through a substance when there is a difference of temperature or of electrical potential.