5 The fifth term of an AP is 26 and its tenth term is 51. Find ap
Answers
Step-by-step explanation:
Given:-
The fifth term of an AP is 26 and its tenth term is 51.
To find:-
Find the AP ?
Solution:-
Let the First term of an AP = a
Let the Common difference = d
Let the Number of terms = n
We know that
The General or nth term of an AP
= an = a+(n-1)d
Now given that
The fifth term of an AP = 26
=> a 5 = 26
=> a+(5-1)d = 26
a+4d = 26 --------------------(1)
and
tenth term of the AP = 51
=> a 10 =51
=> a+(10-1)d = 51
a+9d = 51 ---------------(2)
On subtracting (1) from (2)
=> (2) - (1)
a+9d = 51
a+4d = 26
(-)
___________
0+5d = 25
___________
=> 5d = 25
=> d = 25/5
=> d = 5
On Substituting the value of d in (1) then
=> a+4(5) = 26
=> a +20 = 26
=> a = 26-20
=> a = 6
First term of the AP = 6
Common difference = 5
The general form of an AP = a, a+d,a+2d,...
a= 6
a+d = 6+5 = 11
a+2d = 6+2(5)=6+10=16
The AP : 6,11,16,21,26,...
Answer:-
The Arithmetic Progression for the given problem is 6, 11 , 16 , 21, 26, ...
Check:-
5th term = 6+4(5)=6+20=26
10th term=6+9(5)=6+45=51
Verified the given relations
Used formulae:-
1.The general form of an AP = a, a+d,a+2d,...
2.The General or nth term of an AP = an = a+(n-1)d
3.The First term of an AP = a
The Common difference = d
The Number of terms = n
Answer:
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