Question

find the 9th term from the end (towards the first term) of the Ap 5, 9 ,13 ..... 185 No links please

Answer 1

Hi,

Given A. P is 5 , 9 ,13 , .... 185

Here first term = 5

Common difference = a2 - a1 = 9 -5 = 4

The A.p is 5 , 9 , 13 , ......., 181 , 185

We have find out the 9 th term from the end .

Now , rearrange the A. P

185 , 181 , ......, 13 , 9 , 5

First term = a = 185

Common difference = d = a2 - a1 = 181 - 185 = - 4

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n th term in an A. P = an = a + ( n - 1 ) d

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a = 185 ; d = -4 ; n = 9

9 th term = a9 = a + ( 9-1 ) d

= 185 + 8 × ( - 4 )

= 185 - 32

= 153

Therefore required 9 th term from the end = 153

I hope this will useful to you.

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Answer 2

Solution :-

Given AP is 
5, 9, 13, ........185

Last term of the given AP = 185

Since it is asked in the question to find the 9th term of the AP from the end.

So,
The first term = a = 185, d = - 4 and n = 9

an = a + (n - 1)d

a₉ = 185 + (9 - 1)*-4

⇒ 185 + (8*-4)

⇒ 185 - 32

⇒ 153 

Therefore, 9th term from the end is 153.

Answer.