8 times of the eight term of an arithmetic progression is equal to 12 times of the twelfth term. find its first term if the common difference is -2 .

a₁ = 38

Step-by-step explanation:

Given AP, where:

aₙ = a₁ + (n-1)d

8a₈ = 12a₁₂

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)