SOLUTION: The 11th term of an arithmetic sequence is 57 and the sum of The first and fourth is 29 . 1, Determine the first three terms of the sequence. 2, Determine a formula of the nth

Algebra ->  Sequences-and-series -> SOLUTION: The 11th term of an arithmetic sequence is 57 and the sum of The first and fourth is 29 . 1, Determine the first three terms of the sequence. 2, Determine a formula of the nth       Log On


   

Question 1205669: The 11th term of an arithmetic sequence is 57 and the sum of
The first and fourth is 29 .
1, Determine the first three terms of the sequence.
2, Determine a formula of the nth term.
3,Is 100 a ter
m in the sequence justify your answer
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
ARITHMETIC sequence A%2B%28n-1%29d general term
n is index
d is common difference between terms
A is first term


(fixed)

Description gives the equation system system%28A%2B10d=57%2Cand%2CA%2B%28A%2B3d%29=29%29.

system%28A%2B10d=57%2C2A%2B3d=29%29

system%28A=57-10d%2C2A%2B3d=29%29

2%2857-10d%29%2B3d=29

114-20d%2B3d=29
114-29=17d
d=%28114-29%29%2F17
d=5
-
A=57-10%2A5
A=7
-
general term, highlight%287%2B5%28n-1%29%29;
do what you need from that.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


nth term of an arithmetic sequence formula is:
a%5Bn%5D=a%5B1%5D%2Bd%28n-1%29+ where a%5B1%5D is first term and d is common difference

if the 11th term of an arithmetic sequence is 57, we have
a%5B11%5D=57
a%5B11%5D=a%5B1%5D%2Bd%2811-1%29+
a%5B11%5D=a%5B1%5D%2B10d
then
a%5B1%5D%2B10d=57
a%5B1%5D=57-10d...eq.1

and, if the sum of the first and fourth is 29, we have
a%5B1%5D%2Ba%5B4%5D=29
since
a%5B4%5D=a%5B1%5D%2Bd%284-1%29
a%5B4%5D=a%5B1%5D%2B3d
we have
a%5B1%5D%2Ba%5B1%5D%2B3d=29
2a%5B1%5D=29-3d
a%5B1%5D=29%2F2-3d%2F2....eq.2

from eq.1 and eq.2 we have
57-10d=29%2F2-3d%2F2
114-20d=29-3d
114-29=20d-3d
85=17d
d=85%2F17
d=5

go to
a%5B1%5D=57-10d...eq.1, substitute d
a%5B1%5D=57-10%2A5
a%5B1%5D=57-50
a%5B1%5D=7


1, Determine the first three terms of the sequence.
a%5B1%5D=7
a%5B2%5D=7%2B5=12
a%5B3%5D=7%2B5%2A2=17

2, Determine a formula of the nth term.
a%5Bn%5D=7%2B5%28n-1%29+

3, Is 100 a term in the sequence justify your answer
100=7%2B5%28n-1%29+
100=7%2B5n-5
100=2%2B5n
100-2=5n
98=5n
n=98%2F5
n=19.6+=> 100 is not a term in this sequence because n+is not an integer