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Mathematicians!!! Please Contribute To This Question by mostsimpliest(m): 1:24pm On Nov 23, 2016 |
The sum of the first ten terms of an AP is 15 and the sum of the next ten terms is 215,whats the sum of it 28th term? |
Re: Mathematicians!!! Please Contribute To This Question by dejt4u(m): 1:36pm On Nov 23, 2016 |
mostsimpliest:answer is 546.. a = -7.5 and d = 2 |
Re: Mathematicians!!! Please Contribute To This Question by dejt4u(m): 1:36pm On Nov 23, 2016 |
Re: Mathematicians!!! Please Contribute To This Question by NDSMELODY(m): 2:00pm On Nov 23, 2016 |
Pls show us the workings.......i dnt think dat question is complete.....becos forming an equation leads to simultenous equation which are dsame |
Re: Mathematicians!!! Please Contribute To This Question by dejt4u(m): 2:16pm On Nov 23, 2016 |
NDSMELODY:the question is complete and correct.. The equations and solution will be posted |
Re: Mathematicians!!! Please Contribute To This Question by dejt4u(m): 2:39pm On Nov 23, 2016 |
mostsimpliest:sum of the first ten terms of an AP is 15; S10 = 15; Remember, sum of nth term Sn = n/2 [2a + (n-1)d] Then, S10 = 10/2 (2a + 9d) but S10 = 15, therefore, 10/2 (2a + 9d) = 15, 5(2a+9d) = 15, 2a + 9d = 15/5 2a + 9d = 3.............equation (i) the sum of the next ten terms is 215: this means that S20 - S10 = 215, make S20 the subject of the formula, S20 = 215 + S10 but r'mber that S10 = 15, therefore, S20 = 215 + 15, S20 = 230, again, sum of nth term Sn = n/2 [2a + (n-1)d] Then, S20 = 20/2 (2a + 19d) and Recall that S20 = 230, so, 20/2 (2a + 19d) = 230, 10(2a + 19d) = 230, 2a + 19d = 23............equation (ii) now combine eqn (i) and eqn (ii) together and solve for a and d simultaneously.. 2a + 9d = 3.............eqn (i) 2a + 19d = 23............eqn (ii) elimination method; eqn (ii) minus eqn (i), 0 + 10d = 20, d = 20/10, d = 2 subtitute for the value of d in eqn (i) 2a + 9d = 3.............eqn (i) 2a = 3 - 9d, 2a = 3 - 9(2), 2a = 3 - 18, 2a = -15, a = -15/2, a = -7.5 now a = -7.5 and d = 2.. The question; whats the sum of it 28th term? S28 = ? But sum of nth term Sn = n/2 [2a + (n-1)d] Then, S28 = 28/2 (2a + 27d), S28 = 14 (2(-7.5) + 27(2)), S28 = 14 (-15 + 54), S28 = 14 (39) S28 = 546 ......QED 1 Like |
Re: Mathematicians!!! Please Contribute To This Question by NDSMELODY(m): 3:40pm On Nov 23, 2016 |
Where did u get 20 |
Re: Mathematicians!!! Please Contribute To This Question by dejt4u(m): 3:58pm On Nov 23, 2016 |
NDSMELODY:the sum of the first 10 was given to you.. Then sum of the next 10 will be S20 - S10 |
Re: Mathematicians!!! Please Contribute To This Question by mostsimpliest(m): 5:29pm On Nov 23, 2016 |
dejt4u: nycc1,oil dey ya head |
Re: Mathematicians!!! Please Contribute To This Question by NL1960: 5:43pm On Nov 23, 2016 |
dejt4u: Chai, this brings back fond memories of Additional Mathematics popularly called 'Addico' (now called Further Mathematics) of those days when only hot brains could hold the red coloured Additional Mathematics textbook. . |
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