If nth term of the progression 3,10,17...... and 63,65,67......be same

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