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If the Seventh Term of an A.P. is 1 9 and Its Ninth Term is 1 7 , Find Its (63)Rd Term. - Mathematics

Answer in Brief

If the seventh term of an A.P. is  \[\frac{1}{9}\] and its ninth term is \[\frac{1}{7}\] , find its (63)rd term.

 
  
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Solution

Let a be the first term and d be the common difference.

We know that, nth term = an a + (n − 1)d

According to the question,
 
a7 =  \[\frac{1}{9}\]

⇒ a + (7 − 1)d = \[\frac{1}{9}\]

⇒ a + 6d = \[\frac{1}{9}\]               .... (1)

Also, a9 =  \[\frac{1}{7}\] 

⇒ a + (9 − 1)d = \[\frac{1}{7}\]

⇒ a + 8d =  \[\frac{1}{7}\]    ....(2)

On Subtracting (1) from (2), we get
8− 6d =  \[\frac{1}{7} - \frac{1}{9}\]

⇒ 2= \[\frac{9 - 7}{63}\]
⇒ 2= \[\frac{2}{63}\]
= \[\frac{1}{63}\]
⇒ a = \[\frac{1}{9} - \frac{6}{63}\]          [From (1)]
⇒ a =   \[\frac{7 - 6}{63}\]
⇒ a = \[\frac{1}{63}\]
 
∴ a63 a + (63 − 1)d
        =
\[\frac{1}{63} + \frac{62}{63}\]
 
= \[\frac{63}{63}\]   = 1

Thus, (63)rd term of the given A.P. is 1.
 
 
 
 
 

 

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.4 | Q 43 | Page 26
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