In a test, the value is 1250 units at the first stage and decreases by 55 units at each next stage. At which stage will the value be 260 units?

Correct answer: 19th

This is an arithmetic-progression word problem. The first-stage value is a₁ = 1250, and a decrease of 55 at every next stage means the common difference is d = −55. Thus the value at stage n is aₙ = a₁ + (n − 1)d = 1250 − 55(n − 1). Set this equal to 260: 1250 − 55(n − 1) = 260. Rearranging gives 55(n − 1) = 990, so n − 1 = 18 and n = 19. Checking directly, after 18 decreases the value is 1250 − 18 × 55 = 1250 − 990 = 260. Therefore the value is 260 at the 19th stage, so option C is correct. The negative common difference is essential because the sequence decreases.