Question

Find n so that the nth terms of the following two arithmetic sequence are same.1,7,13,19... and100,95,90...

Answer 1

this is Ur required result

Answer 2

Answer:

10

Step-by-step explanation:

Sequence 1 : 1,7,13,19...

First term = a  = 1

Common difference = d = 7-1 = 13-7 = 6

Formula of nth term in A.P. :$a_n=a+(n-1)d$

Where a = first term

d = common difference

So, nth term of Sequence 1 :

$a_n=1+(n-1)6$

Sequence 2: 100,95,90...

First term = a  = 100

Common difference = d = 95-100 = 90-95 = -5

Formula of nth term in A.P. :$a_n=a+(n-1)d$

Where a = first term

d = common difference

So, nth term of Sequence 1 :

$a_n=100+(n-1)(-5)$

$a_n=100-5(n-1)$

Since we are given that the nth terms of the following two arithmetic sequence are same.

⇒$100-5(n-1) = 1+(n-1)6$

⇒$100-5n+5= 1+6n-6$

⇒$105-5n= 6n-5$

⇒$105+5= 6n+5n$

⇒$110=11n$

⇒$\frac{110}{11}=n$

⇒$10=n$

Hence the value of n is 10