Question

if nth term of the progression 3,10,17...... and 63,65,67......be same then find the value of n.

Answer 1

Answer:

n=13

Step-by-step explanation:

1) 3,10,17......

First term = a = 3

Common difference = d = 10-3 = 17-10 = 7

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

Substitute the values :

$a_n=3+(n-1)7$

$a_n=3+7n-7$

$a_n=7n-4$  ---A

2) 63,65,67......

First term = a = 63

Common difference = d = 65-63= 67-65 = 2

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

Substitute the values :

$a_n=63+(n-1)2$

$a_n=63+2n-2$

$a_n=61+2n$  --B

Now we are given that the nth term of both the progression are same

Equate A and B

So, $61+2n=7n-4$

$65 = 5n$

$13 = n$

Hence the value of n is 13

Answer 2

Refers to attachment ☻☻