First 10 Terms Of The Arithmetic Sequence 10.2, 12.7, 15.2, 17.7, ...
First 10 terms of the Arithmetic Sequence 10.2, 12.7, 15.2, 17.7, ... 10.2 , 12.7 ,15.2 ,17.7 ,20.2 ,22.7, 25.2 ,27.7 ,30.2 ,32.7 10th term: 32.7
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Sun Of An Object Is Dropped From The Top Of A Building And Falls 16ft. In The 1st Second. It Falls Three Times As Far During The 2nd Second, Five Time
sun of an object is dropped from the top of a building and falls 16ft. in the 1st second. it falls three times as far during the 2nd second, five times as far during the 3rd second, and so on in arithmetic sequence. how far will it have fallen in 10 seconds? Answer: The object will have fallen 304 feet in 10 seconds. Step-by-step explanation: The time in seconds is the term or nth term, n. The distance in feet is the corresponding sequence. To find the arithmetic sequence: a₁ = 16 ft a₂ = 16×3 = 48 ft (3 times as far as the distance on the first second.) a₃ = 16×5 = 80 ft (5 times as far as the distance on the first second.) To solve for the common difference (d): a₂-a₁ = a₃-a₂ 48-16 = 80-48 32 = 32 The arithmetic sequence: 16, 48, 80 The common difference (d): 32 Arithmetic sequence general rule: an = a₁ + (n-a)(d) Where: an = last term n = the term o nth position in the sequence a₁ = the first term d = common difference Find the distance on the 10th second, n=10: a₁₀ = ...
What Is The Solution Of This Answer??
What is the solution of this answer?? First, lets factor it out. Lets find the factors of 9, we have 1, 9. Then, lets find the factors of d^2, it gives us d and another d. Make 2 parentheses. ( )( ) Fill it with 2 "d"s (d )(d ) Since the quadratic equations operations are all addition put the symbol "+" in the parentheses, right after d. (d + )(d + ) Next, put 1 and 9 after the "+" symbol (d + 1)(d + 9) Lets check if its right! Apply the FOIL METHOD F = d • d O = 9 • d I = 1 • d L = 9 Resulting to, d^2 + 9d + d + 9 Then simplify d^2 + 10d + 9 So its correct! Finally, separate the two factors (d + 1) --- (d + 9) Do this, (d + 1) = 0 (d + 9) = 0 Equate the two "d"s On the first equation, subtract 1 to both sides making d = -1 On the second equation, subtract 9 to both sides making d = -9 There you have it! The solutions are -1 and -9
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