Question

determine the ap whose third term is 16and difference of 7th and 5th term is 12

Answer 1

a3 = 16
a + 2d = 16 --------- equation 1

a7 - a5 = 12
a + 6d - a - 4d = 12
2d = 12
d = 6 putting the value in equation 1

a + 2 × 6 = 16
a = 16 - 12
a = 4.

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Answer 2

here....

t3=a+2d=16
so,
a+2d=16.....................(1)

by the second given condition.

t7-t5=12
(a+6d)-(a+4d)=12
a+6d-a-4d=12
2d=12
d=12/2
d=6


now, substitute d=6 in equation no. (1)

a+2d=16
a+2(6)=16
a+12=16
a=16-12
a=4


now,we have,
a=4 ,
d=6

A.P:
t1=a=4
t2=a+d=10
t3=a+2d=16
t4=a+3d=22

4,10,16,22,........... is the required ARITHMETIC PROGRESSION (A.P)


hope this helps!!!