2 2
The sum of the first 20 terms of an arithmetic progression is 405 and the sum of the first 40 terms
is 1410.
Find the 60th term of the progression.

94.5

Step-by-step explanation:

sₙ = n/2 * (2a₁ + (n-1)d) ... Sₙ: sum of first n term   d: common difference

sum of the first 20 terms: 20/2 * (2a₁ + (20-1)d) = 10* (2a₁+19d) = 405

2a₁+19d = 40.5   ... (1)

sum of the first 40 terms: 40/2 * (2a₁ + (40-1)d) = 20* (2a₁+39d) =1410

2a₁+39d = 70.5    ... (2)

(2)-(1): 20d = 30

d = 1.5              

a₁ = 1/2 (40.5 - 19*1.5) = 6

aₙ = a₁ + (n-1)d

60th term: a₆₀ = 6 + (60-1)*1.5 = 94.5

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula