Karteikarten
Arithmetic Sequences and Series
Karten in diesem Stapel (14)
- 1The common difference of an arithmetic sequence is defined by....d
- 2The first of an arithmetic sequence is given by....a
- 3How do we find any term of an arithmetic sequence?a+(n-1)d
- 4In general, an arithmetic sequence looks like:a , a+d , a+2d , a+3d ...... , a+(n-1)d
- 5If a=7 and d=5 , find the 10th term of the arithmetic sequence7+(10-1)5 = 52
- 6The 5th term of an arithmetic sequence is 50 and the 8th is 92. Find a and d.a + (5-1)d = 50 , a + (8-1)d = 92
a+4d=50
a+7d=92
Solve simultaneously for a=-6 and d=14 - 7What is an arithmetic series?The sum of the terms in an arithmetic sequence
- 8In general, what does an arithmetic series look like?Sn = a + (a+d) + (a+2d) + .... + a+(n-1)d
- 9How do we find the sum of an arithmetic series?Sn = 1/2 n(2a+(n-1)d)
OR
Sn = 1/2 n(a+l)
(a= first term, l=last term) - 10The arithmetic series: 51+58+65+72+...+1444 has 200 terms. Find the 101st term and also the sum of the last 100 termsa=51 , d=7
u101 = 51 + (101-1)7 = 751
Last 100 terms = S200 - S100 , so:
0.5(200)(2x51+(200-1)7) - 0.5(100)(2x51+(100-1)7 = 109750 - 11What is another way we could calculate the sum of the last 100 terms for the question above?Use u101 = 751 ; a=751 , d=7 , n=100
So: 0.5(100)(2x751 + (100-1)7) = 109750 - 12The 25th term of an arithmetic series is 38. The sum of the first 40 terms is 1250. Show the common difference is 1.5 and the first term is 2.a+(25-1)d = 38 , a+24d = 38
0.5(40)(2a+(40-1)d) = 1250 , so 4a+78d=125
Solve these 2 equations simultaneously for a=2 and d=3/2 - 13For the values above, find the number of terms in the series which are less than 1002 + (n-1)1.5 < 100 , rearrange for n<199/3
199/3 = 66 + 1/3 , so the number of terms less than 100 = 66 (ignore 1/3 as not integer) - 14The nth term of an arithmetic series is 8n-6 , find the sum of the first 20 terms.First term = 8(1)-6 = 2
Last term = 8(20)-6 = 154
Therefore: 0.5(20)(2+154) = 1560
Informationen
- Beschreibung
- Arithmetic Sequences and Series
- Erstellt von
- Doc Boff · Jul 2019
- Aktualisiert
- 24 Sep 2019
- Aufrufe
- 23
- Bewertung