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The second term of an arithmetic sequence is 7. The sum of the first four terms of the arithmetic sequence is 12. Find the first term, a, and the common difference, d, of the sequence.

Let a be the first term

Let d be the common difference

a + d = 7

S4 = 4/2 (2a +3d) = 12

Simultaneous equation:

a+d =7 // x 6
4a +6d = 12

Differen...

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Answered by Alexander T. Maths tutor
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Abstracting Reasoning is a section of the UKCAT that is hated by students. There is no real way to learn it; either this sort of thing works for you, or it is a nightmare.

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Newton's Law of Gravitation states: F=GMm/r^2, where G is the gravitational constant (6.67×10−11m^3kg^−1s^−2). Kepler's Third Law, states t^2=kR^3. The mass of the sun is 1.99x10^30kg. Find the value of k and its units

F=GMm/r2=mv2/r, v=2pir/t

equating the two values for F and remembering to include the equation for v, GMm/r^2 = m(2pir/t^2)^2/r. Rearranging to find t^2, t^2 = 4pi^...

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Answered by Sam B. Physics tutor
17334 Views

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