This is an arithmetic sequence since there is a common difference between each term. In this case, adding <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to the previous term in the sequence gives the next term. In other words, <math><mstyle displaystyle="true"><msub><mi>a</mi><mrow><mi>n</mi></mrow></msub><mo>=</mo><msub><mi>a</mi><mrow><mn>1</mn></mrow></msub><mo>+</mo><mi>d</mi><mrow><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> .

Arithmetic Sequence: <math><mstyle displaystyle="true"><mi>d</mi><mo>=</mo><mn>3</mn></mstyle></math>

This is the formula of an arithmetic sequence.

Substitute in the values of <math><mstyle displaystyle="true"><msub><mi>a</mi><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>d</mi><mo>=</mo><mn>3</mn></mstyle></math> .

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

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