If the nth term of the A.P. 9,7,5,… is same as the nth term of the A.P. 15,12,9,… Find n.
Step 1: Finding the nth term of the A.P. 9,7,5,…:
Here, a=9 and d=-2
an=a+n-1d⇒an=9+n-1-2⇒an=9-2n+2⇒an=11-2n
Step 2: Finding the nth term of the A.P. 15,12,9,…:
Here, a=15 and d=-3
an=a+n-1d⇒an=15+n-1-3⇒an=15-3n+3⇒an=18-3n
Step 3: Equating nth term of both the A.P.'s:
11-2n=18-3n⇒3n-2n=18-11⇒n=7
Hence, the value of n is 7.
If the nth term of the A.P. 9,7,5,... is same as the nth term of the A.P. 15,12,9,... find n.
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