2. The 10th term of an A.P 5,9,13......
(A)2
(B)-2
(c) 6
(d) -6
Answers
Answer:
-2 is the correct answer
Step-by-step explanation:
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Answer :
a(10) = 41
Note :
★ A.P. (Arithmetic Progression) : A sequence in which the difference between the consecutive terms are equal is said to be in A.P.
★ If a1 , a2 , a3 , . . . , an are in AP , then
a2 - a1 = a3 - a2 = a4 - a3 = . . .
★ The common difference of an AP is given by ; d = a(n) - a(n-1) .
★ The nth term of an AP is given by ;
a(n) = a + (n - 1)d .
★ If a , b , c are in AP , then 2b = a + c .
★ The sum of nth terms of an AP is given by ; S(n) = (n/2)×[ 2a + (n - 1)d ] .
or S(n) = (n/2)×(a + l) , l is the last term .
★ The nth term of an AP can be also given by ; a(n) = S(n) - S(n-1) .
Solution :
- Given AP : 5 , 9 , 13 , . . .
- To find : 10th term , a(10) = ?
Clearly ,
First term , a = 5
Common difference , d = 9 - 5 = 4
Also ,
We know that , the nth term of an AP is given as ; a(n) = a + (n - 1)d
Thus ,
The 10th term of the AP will be ;
=> a(10) = a + (10 - 1)d
=> a(10) = a + 9d
=> a(10) = 5 + 9•4
=> a(10) = 5 + 36
=> a(10) = 41