Mathematics

1 ) drop the arithmetical sequence of poem 1 , 3 , 5 , 7 , 9 . to point out the followinga ) What is d , the divagation mingled with any 2 margesAnswer : d 2Show bring in out in this spaced 3-1 5-3 7-5 9-7 2b ) Using the manifestation of the ordinal number status of an arithmetic sequence , what is the 10 inaugural end pointAnswer : n-th enclosure 201Show establish in this spacean a (n-1 ) d , wherea initiatory bound 1d difference between 2 terms 2n 24an 1 (101-1 )2 1 blow (2 1 200 201c ) Using the formula for the metre of an arithmetic series , what is the pith of the stolon 20 termsAnswer : Sn 400Show scarper in this spaceSn n /2 (a1 an , wheren 20a1 foremost term 1an nth terman 1 (20-1 )2 1 (19 )2 1 83 39Sn 20 /2 (1 39 10 (40 400d ) Using the formula for the entireness of an arithmetic series , what is the make sense of the first 30 termsAnswer : Sn 900Show arrive at in this spaceSn n /2 (a1 an , wheren 20a1 world-class term 1an nth terman 1 (30-1 )2 1 (29 )2 1 58 59Sn 30 /2 (1 59 15 (60 900e ) What observation gouge you make well-nigh these sums of this series (HINT : It would be beneficial to find a a couple of(prenominal) more sums like the sum of the first 2 , hence the first 3 , etc ? extinguish your observations as a normal formula in nAnswer : Sn (n )[2a (n-1 )d] /2Show spiel in this spaceThe sum of terms increases as more terms are added .

The sum of n terms is n times the average of the 1st and the nth term Sn (n (a an /2 , wherea 1st terman a (n-1 ) ! dSn (n (a an /2 (n )[a a (n-1 )d] /2 (n )[2a (n-1 )d] /22 ) call the geometric sequence of meter 1 , 2 , 4 , 8 . to find the followinga ) What is r , the ratio between 2 consecutive termsAnswer : r 2Show civilise in this spacer 2 /1 4 /2 8 /4 2b ) Using the formula for the nth term of a geometric sequence , what is the twenty-fourth termAnswer : an 8388608Show work in this spacean a1rn-1 , wheren 24a1 1st term 1r ratio between 2 terms 2an 1 224-1 223 8388608c ) Using the formula for the nth term of a geometric sequence , what is the sum first 10 termsAnswer : Sn 1023Show work in this spaceSn a1 (rn-1 / r-1 , wheren 10a1 1st term 1r ratio between 2 terms 2Sn 1 (210 -1 (2-1 10233 ) Use the geometric sequence of numbers 1 , 1 /2 , 1 /4 , 1 /8 . to find the followinga ) What is r , the ratio between 2 consecutive termsAnswer : r 1 /2Show work in this space...If you ask to get a liberal essay, order it on our website: OrderCustomPaper.com

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