Attempt following question by selecting a choice to answer.
B
The length of the arc of the swing of a pendulum is 308 mm. If the length of the arc of each succeeding swing is decreasing by 30%, then find the total length the pendulum swings before it stops.
eee BBBA.
B674.52 mm
B.
B1026.66 mm
C.
B440 mm
D.
BCannot be determined
BB
B
Step 1: Since the length of the arc of each succeeding swing is decreased by 30%, the length of each successive arc becomes 70% of the previous arc. The length of the arcs forms a geometric sequence: 308, 215.60, 150.92, ...[Analyse and understand the problem.]
Step 2: S = a1(1 - r)[Use the formula for the sum of an infinite geometric series.]
Step 3: S = 308(1 - 0.70)[a1 = 308, r = 70% = 0.70.]
Step 4: S = 3080.30
Step 5: S = 1026.66
Step 6: The total length the pendulum swings before it stops is 1026.66 mm.