Question

the 9th term of an ap is equals to 6 time of its second term if the fifth term is 22 find the AP​

Answer 1

Answer:

the ap is:2, 7, 12, 17...

Detailed Solution:

https://www.shaalaa.com/question-bank-solutions/the-9th-term-ap-equal-6-times-its-second-term-if-its-5th-term-22-find-ap-sum-first-n-terms-ap_63402

Answer 2

EXPLANATION.

• GIVEN

9th term of an Ap is equal to 6 times of its

2nd term.

5th term is 22

TO FIND THE AP.

Formula of Nth terms of an Ap.

=> An = a + ( n - 1 ) d

=> case = 1

=> T9 = 6 ( T2)

=> a + 8d = 6 ( a + d)

=> a + 8d = 6a + 6d

=> 8d - 6d = 6a - a

=> 2d = 5a ...... (1)

=> case = 2

=> T5 = 22

=> a + 4d = 22

=> a = 22 - 4d ........ (2)

From equation (1) and (2) we get,

put the value of equation (2) in equation (1)

we get,

=> 2d = 5 ( 22 - 4d )

=> 2d = 110 - 20d

=> 22d = 110

=> d = 5

put the value of d = 5 in equation (1)

we get,

=> 2 ( 5 ) = 5a

=> 10 = 5a

=> a = 2

Therefore,

Tn term = a + ( n - 1 ) d

Algebraic expression of an Ap

=> An = 2 + ( n - 1 ) 5

=> An = 2 + 5n - 5

=> An = 5n - 3

Therefore,

An = 5n - 3

put n = 1 we get,

=> 5(1) - 3 = 2

put n = 2 we get,

=> 5(2) - 3 = 7

put n = 3 we get,

=> 5(3) - 3 = 12

put n = 4 we get,

=> 5(4) - 3 = 17

Therefore,

series are = 2 , 7 , 12 , 17 ..........