for what value of nth term of two AP's 65,70,75 & 5,14, 23 are equal
Answers
Step-by-step explanation:
Given :-
Two AP's 65,70,75 & 5,14, 23
To find :-
For what value of nth term of two AP's 65,70,75 & 5,14, 23 are equal ?
Solution :-
Given that :
First A P : 65,70,75,...
First term = a = 65
Common difference= d = 70-65 = 5
We know that
nth term of an AP = an = a+(n-1)d
=> an = 65+(n-1)5
=> an = 65 + 5n -5
=> an = 65-5+5n
=> an = 60+5n
Therefore,nth rem of the first AP = 5n+60 -----(1)
Second AP :5,14,23,...
First term = a = 5
Common difference = d = 14-5 =9
We know that
nth term of an AP = an = a+(n-1)d
=> an = 5+(n-1)9
=> an = 5 + 9n -9
=> an = 5-9+9n
=> an = (-4)+9n
Therefore,nth rem of the second AP = 9n-4 ---(2)
Let both nth terms are equal
=> (1) = (2)
=>5n +60 = 9n -4
=> 9n -5n = 60+4
=> 4n = 64
=> n = 64/4
=> n = 16
so, required value of nth term = 16th term
Answer:-
For 16th both given AP's are equal.
Check :-
16th term of the first AP :65,70,75,..
a 16 = a+15d
=> 65+15(5)
=> 65+75
=> 140
a 16 = 140
and
16th term of the second AP :5,14, 23
a 16 = a+15d
=> 5+15(9)
=> 5 + 135
=> 140
Both 16 th terms are equal
Verified the given relations in the given problem
Used formulae :-
- nth term of an AP = an = a+(n-1)d
Where,
- a = First term
- d = Common difference
- n = number of terms
Answer:
For 16th both given AP's are equal.