Question

If the 8th term of an ap 31 and fifth term is 16 more than the 11th term find the ap and solution

Answer 1

let a be the 1st term and d be the common difference 


a8 = a + 7d = 31 

a15 = a + 14d = a11 + 16
                         (a + 10d) + 16

a + 10d +16 = a + 14d 

= a + 10d +16 = a + 10d + 4d

= 16 = 4d 
 d = 16/4 = 4

....... ...... ....... .... ........ .....
 
a + 7d = 31

a + 7(4) = 31

a + 28 = 31 
a = 31 -28 = 3

......... ........ ...... .........
 
a = 3 , d = 4 ...

therefore Ap = a , a+d , a+2d ,a+3d ......

                    = 3 , 3+4 ,3+2(4) , 3 + 3(4)
 
                     = 3 , 7 , 11 , 15 .......

HOPE U GOT IT !! CHEERS KS !

Answer 2

let the first term of an ap be a and common difference be d

a8=31
a5=16+a11
a+4d=16+a+10d
4d=16+10d
4d-10d=16
-6d=16
d=-16/6
d=-8/3. = 2.6
a8=31
a+7d=31
a+7×[-2•6]=31
a-18.2=31
a=31+18.2
a=49.2

AP=49.2,46.6,44,.........