Which term of the Arithmetic Progression 3, 10, 17, ... will be 84 more than its 13 th term?
10 points for the best answer!
2006-08-12 23:39:12 · 6 answers · asked by Amanda 1 in Education & Reference ➔ Homework Help
Any term will be given by the formula
T(n) = a+(n-1)d
Where a is the first term, n is the number of terms and d the difference between successive terms.
In this case, a = 3, d = 7.
therefore the 13th term is 3 + 13 * 7 which = 94
84 + 94 = 178
T(n) = 178 = 3 + 7(n-1)
175 = 7n-7
168 / 7 = n
n = 24
The 24th term is 84 more than the 13th term.
2006-08-13 00:36:30 · answer #1 · answered by jemhasb 7 · 0⤊ 0⤋
Previous answers were almost right.
The formula for the nth term of an arithmetic sequence is
t = a + d(n - 1), where a is the first term, d is the common difference, and n is the number of the term. The first term is 3, so a = 3. you add 7 to go from term to term, so d = 7. To find the 13th term, n = 13. To find the thirteenth term, you would say
t = 3 + 7( 13 - 1 )
t = 3 + 7(12)
t = 3 + 84
t = 87, so 87 is the 13th term.
The number that is 84 more than 87 would be 84 + 87 or 171.
So now you are saying if a term is 171 when the first term was 3 and the difference was 7, what is the value of n? This equation is:
171 = 3 + 7( n - 1)
171 = 3 + 7n - 7
171 = 7n - 4
175 = 7n
25 = n
So the term that is 84 more than the 13th term is the 25th term.
Another way to get to the same place is to say if a number must be 84 more than the 13th term and you increase by 7 each time you go to the next number, how many 7s are there in the total change of 84? 84 divided by 7 = 12, so you must go 12 places past the 13th spot, which is 13 + 12 or the 25th place!
2006-08-13 01:28:58 · answer #2 · answered by Pi R Squared 7 · 0⤊ 0⤋
Formula for AP ;;;;; a + (n-1)d
here a =3......d = 7......n unknown
13th term = a+ 12d = 3 + 84 = 87
13th term + 84 = 171
we need to find 'n' now
171 = 3 + (n-1)7
168 = (n-1)7
n-1 = 24
n = 25
Therefore, its the 25th term
2006-08-14 07:46:07 · answer #3 · answered by M.S.N. 2 · 0⤊ 0⤋
nth term = first term + (common difference)*("n" minus one)
= a + d*(n-1)
=3 + (7)(12)
=87
so,
x = 94 + 87 = 181
and for that term,
181 = 3 + (7)(n-1)
178 = 7(n-1)
24 = n - 1
n = 25
2006-08-13 14:11:23 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Maaan. This is a difficult problem. U need to pay consultation fee to a math professor. Cant resolve in return for 10 points. BTW u cant buy pasta with this 10 points.
2006-08-12 23:44:48 · answer #5 · answered by Anonymous · 0⤊ 0⤋
t13=a+12d=3+7*12=87
171=3+7n
n=24
the 24thterm
2006-08-12 23:43:55 · answer #6 · answered by raj 7 · 0⤊ 0⤋