for example,
1st sequence-1,8,15, ....., 1975
2nd sequence-2,13,24, ...., 1982
So, how do I find out the no of common terms in these A.Ps?
How to find no of common terms in 2 arithmetic progressions?
2016-05-09 7:17 pm
回答 (2)
2016-05-09 7:47 pm
For the first A.P. : 1, 8, 15, ....., 1975
The first term, T(1) = a = 1
Common difference, d = 8 - 1 = 15 - 8 = 7
T(n) = 1975
a + (n - 1) d = 1975
1 + 7 (n - 1) = 1975
7 (n - 1) = 1974
n - 1 = 282
n = 283
Number of terms, n = 283
====
For the first A.P. : 2, 13, 24, ...., 1982
The first term, T(1) = a = 2
Common difference, d = 13 - 2 = 24 - 13 = 11
T(n) = 1982
a + (n - 1) d = 1982
2 + 11 (n - 1) = 1982
11 (n - 1) = 1980
n - 1 = 180
n = 181
Number of terms, n = 181
The first term, T(1) = a = 1
Common difference, d = 8 - 1 = 15 - 8 = 7
T(n) = 1975
a + (n - 1) d = 1975
1 + 7 (n - 1) = 1975
7 (n - 1) = 1974
n - 1 = 282
n = 283
Number of terms, n = 283
====
For the first A.P. : 2, 13, 24, ...., 1982
The first term, T(1) = a = 2
Common difference, d = 13 - 2 = 24 - 13 = 11
T(n) = 1982
a + (n - 1) d = 1982
2 + 11 (n - 1) = 1982
11 (n - 1) = 1980
n - 1 = 180
n = 181
Number of terms, n = 181
2016-05-10 8:36 am
Number of terms, n = 181
收錄日期: 2021-04-18 14:49:21
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20160509111731AAaQTni