Question

If 7^( th ) term of an A.P is 9 and 9^( th ) term of the A.P is 7 then 20^( th ) term of the A.P is​

Answer 1

Step-by-step explanation:

Given :-

7th term of an AP is 9.

9th term of the AP is 7.

To find:-

Find 20th term of the AP ?

Solution :-

Let the first term of an AP = a

Let the Common difference of the AP = d

We know that

The general term of the AP = an = a+(n-1)d

Given that

7th term of an AP is 9.

=> a 7 = 9

=> a+(7-1)d = 9

=> a + 6d = 9 --------------(1)

and

9th term of the AP is 7.

=> a 9 = 7

=> a+(9-1)d = 7

=> a+8d = 7----------------(2)

On Subtracting (2) from (1) then

(1)-(2)=>

a + 6d = 9

a + 8d = 7

(-)

_________

0 -2d = 2

_________

=> -2d = 2

=> d = 2/-2

=> d = -1

Common difference = -1

On Substituting the value of d in (1) then

a + 6(-1) = 9

=> a -6 = 9

=> a = 9+6

=> a = 15

First term = 15

Now ,

20th term of the AP

=> a 20 = a+(20-1)d

=> a 20 = a +19d

=> a 20 = 15+(19)(-1)

=> a 20 = 15+(-19)

=> a 20 = 15-19

=> a 20 = -4

Answer:-

20th term of the AP is -4

Used formulae:-

• The general term of the AP
• = an = a+(n-1)d
• a = first term
• d = Common difference
• n=number of terms