If you were given the fourth and the twenty-first terms of an arithmetic sequence how would you find the first term?
2006-12-15 03:25:27 · 10 answers · asked by fgfd j 1 in Science & Mathematics ➔ Mathematics
http://en.wikipedia.org/wiki/Arithmetic_sequence
2006-12-15 03:42:10 · answer #1 · answered by Randy 4 · 0⤊ 0⤋
Raj seems correct; however, you can solve his eqtns directly for term1 (which he's calling t1). This seems to be what mandeep did. rhsaunders final eqtn corresponds to Raj's first eqtn where
F(4) = t4; F(1) = t1 and 3a = 3d
aksh...'s asterisk needs to be an addition sign.
The more critical thing, IMHO, with arithmetic sequences is that the common difference ALWAYS comes from subtracting a trailing term (lower positioned term) from it's adjacent leading term (higher positioned term).
2006-12-15 04:27:45 · answer #2 · answered by answerING 6 · 0⤊ 0⤋
First response is not correct. Let F(n) be the value of the nth element of the series. Then F(n+1) = F(n) + a, where a is the difference between terms. Then F(21) = F(4) + 17a. Obviously, F(1) = F(4) - 3a.
2006-12-15 03:32:29 · answer #3 · answered by Anonymous · 0⤊ 2⤋
T2 = a + d 7 = a + d ------- (a million) (a = 1st time period, d = elementary vast difference , T2 = second time period, T4 = 4th time period) T4 = a + 3D 8 = a + 3D ------- (2) lets remedy those simultaneous equations, (a million) x 3, 21 = 3a + 3D --------- (3) lets subtract (2) from (3), 13 = 2a a = 6.5
2016-11-30 19:44:11 · answer #4 · answered by ? 4 · 0⤊ 0⤋
that means there are17terms in betwen them.
U know the difference between them.Divide the difference by 17 and u will get d(common difference).Then u can find the first term(a) easily by using this formula
nth term=a*(n-1)d
4th term=a*3d
2006-12-15 03:33:07 · answer #5 · answered by aksh_1991 2 · 0⤊ 0⤋
You can tell them that the 1st term is Apple Pie. There is not enough information given to answer the question unless you assume some things.
Although the answer the people are looking for is your approach to the problem and the assumptions you are making.
2006-12-15 03:32:26 · answer #6 · answered by Andrew E 2 · 0⤊ 2⤋
t4 = t1 + 3d (equation1)
t21 = t1 + 20d (equation2)
Multiply equation1 with '20' and equation2 with '3' and subtract
20*t4 - 3*t21 = 20*t1 - 3*t1 +60*d - 60*d
=> 20*t4 - 3*t21 = 17*t1
=> t1 = (20*t4 - 3*t21 )/17
2006-12-15 03:38:07 · answer #7 · answered by mandeep 3 · 0⤊ 0⤋
t1 = a + 3d
t2 = a+20d
d = (t2-t1) /17
Thus find out a.
2006-12-15 03:35:36 · answer #8 · answered by ag_iitkgp 7 · 0⤊ 0⤋
t4=t1+3d
t21=t1+20d
subtracting
t21-t4=17d
d can be obtained
substituting find t1
2006-12-15 03:28:27 · answer #9 · answered by raj 7 · 0⤊ 1⤋
you got my vote raj
2006-12-15 03:34:52 · answer #10 · answered by wind cries mary 3 · 0⤊ 0⤋