Question

For what value of nth terms of the following two APs the same 13,19,25........and 69,68,67.......?Also find this term...?​

Answer 1

Answer:

Step-by-step explanation:

First series = 13,19,25............

nth term = 13+(n-1)6 = 13+6n-6=6n+7

Second Series = 69,68,67........

nth term = 69+(n-1)(-1)= 70-n

So 6n+7=70-n

7n=63

n=9

9th term will be equal which is equal to 61

Answer 2

Given:-

• 13,19,25......and 69,68,67.....have their nth value are same( their last term will be equal)

To find:-

• value of n = ....?

Solution:-

Let nth term of the given progresion be l and L respectively.

The first AP is 13,19,25.....

Let its first term be a and common difference be d.Then,

a=13 and d=(19-13)=6.

So, its nth term is given by

l = a+(n-1)d

=> l = 13+(n-1)6

=> l = 13+6n-6

=> l = 6n+7

The second AP is 69,68,67.....

Let its first term be A and common diffrence be D.Then,

A=69 and D=(68-69)= -1

So, its nth term is given by

L=A+(n-1)D

=> L = 69+(n-1)(-1)

=> L = 69-n+1

=> L = 70-n

Now , L = l

=> 6n+7 = 70-n

=>6n+n = 70-7

=> 7n = 63

=> n=9

Hence , the 9th term of each AP is same.

This term = 70-9=61. [ L = 70-n ]

Hope its help uh❤