3rd term of an arithmetic sequence is 9 and 9th term is 3. find the sequence
Answers
Answer:
Correct option is
A
4n−1 and T9=35
We know,
nth term an=a+(n−1)d
a= First term
d= Common difference
n= number of terms
an=nth term
Here,
a=3 and d=7−3 or 11−7=4
an=a+(n−1)d=3+(n−1)4
an=4n−1
For 9th term put n=9
T9=a9=4×9−1=35
Step-by-step explanation:
Given :-
3rd term of an arithmetic sequence is 9 and 9th term is 3.
To find :-
Find the sequence ?
Solution :-
Let the first term a and the common difference is d of an AP
We know that
nth term of an AP = an = a+(n-1)d
Third term of the AP = 9
=> a3 = 9
=> a+(3-1)d = 9
=> a + 2d = 9 -------------(1)
and
Ninth term of the AP = 3
=> a9 = 3
=> a+(9-1)d = 3
=> a +8d = 3 ------------(2)
On subtracting from (2) from (1) then
a + 2d = 9
a + 8d = 3
(-) (-) (-)
_________
0 -6d = 6
_________
=> -6d = 6
=> d = 6/-6
=> d = -6/6
=> d = -1
Common difference = -1
On substituting the value of d in (1) then
=> a +2(-1) = 9
=> a -2 = 9
=> a = 9+2
=> a = 11
First term = 11
The general form of an AP = a , a+d, a+2d, ...
a = 11
a+d = 11+(-1) = 11-1 = 10
a+2d = 11+2(-1) = 11-2 = 9
The AP : 11, 10 , 9, ...
Answer :-
The Arithmetic Progression for the given problem is 11, 10 , 9, ...
Check:-
We have ,
a = 11 , d = -1
a3 = a+2d = 11+2(-1) = 11-2 = 9
and
a9 = a+8d = 11+8(-1) = 11-8 = 3
Verified the given relations in the given problem.
Used formulae:-
- The general form of an AP = a , a+d, a+2d, ...
- nth term of an AP = an = a+(n-1)d
- a = First term
- d = Common difference
- n = Number of terms