finf n so that nth terns of the following two A.P's are the same
1,7,13,19,....... and 100,95,90......
Answer :
We have two A.P. As : 1,7,13,19,....... and 100,95,90......
We know formula for nth term in A.P.
an = a1 + ( n - 1 ) d
Where a1 = first term of the series
d = Common difference
So nth term for first series As a1 = 1 And d = 6, we get
an = 1 + ( n - 1 ) 6
an = 1 + 6n - 6
an = 6n - 5
And , nth term for Second series As a1 = 100 And d = - 5, we get
an = 100 + ( n - 1 ) ( - 5 )
an = 100 - 5n + 5
an = 105 - 5n
According to question we want to find n for nth of both series is same , so we equate both equation and get
6n - 5 = 105 - 5n
11n = 110
n = 10
So,
10th term of both series is same . ( Ans )
We have two A.P. As : 1,7,13,19,....... and 100,95,90......
We know formula for nth term in A.P.
an = a1 + ( n - 1 ) d
Where a1 = first term of the series
d = Common difference
So nth term for first series As a1 = 1 And d = 6, we get
an = 1 + ( n - 1 ) 6
an = 1 + 6n - 6
an = 6n - 5
And , nth term for Second series As a1 = 100 And d = - 5, we get
an = 100 + ( n - 1 ) ( - 5 )
an = 100 - 5n + 5
an = 105 - 5n
According to question we want to find n for nth of both series is same , so we equate both equation and get
6n - 5 = 105 - 5n
11n = 110
n = 10
So,
10th term of both series is same . ( Ans )