For what value of n is the nth term of following two A.P.s are same.i) 1, 7 , 13..; 69,68, 67..
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Solution : The frequency of a class can be obtained by simply counting the number of observations that are falling in the interval. Class mid points is given by, Class mid point…
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Clearly, 1,7,13,19,.... forms an A.P. with first term 1 and common difference 6. Therefore, its n
th
term is given by
a
n
=1+(n−1)×6=6n−5
Also, 69,68,67,.... forms an A.P. with first 69 and common difference −1.
So, its n
th
term is given by
a
n
′
=69+(n−1)×(−1)=−n+70
The two A.P's will have identical n
th
terms, if
a
n
=a
n
′
⟹6n−5=−n+70
⟹7n=75
⟹n=
7
75
which is not a natural number.
Hence, there is no value of n for which two A.P's will have identical terms.
Step-by-step explanation:
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