# And there was an AP

Algebra Level 2

A finite arithmetic progression of n terms have this properties:

$${ a }_{ 2 }+{ a }_{ 11 }= 78$$

$${ a }_{ 4 }+{ a }_{ 8 }= 72$$

$$\sum _{ k=1 }^{ n }{ { a }_{ k } } =468$$

Find the common difference and the number of terms.

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