Question

The 7th tern of ap is -4and 13th term -16 .find the A .P

Answer 1

As per question,

t7 = -4

a + 6d = -4 -------(1)

Again,

t13 = -16

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

Subtracting (2)-(1)

a+ 12d = -16

-(a+6d) = -4

+ - +

___________

6d = -12

d = -2

Putting the value of 'd' in equation (1)

a + 6d = -4

a + 6(-2) = -4

a -12 = -4

a = -4+12

a = 8

Therefore,

A.P.

= a, a+d, a+2d..........

= 8, 6 , 4........

Answer 2

Answer:

A.P is 8,6,4,2,.......

Step-by-step explanation:

t7= -4 & t13= -16

using, tn = a+(n-1)d

t7 = a+(7-1)d

-4 = a+7d-d

-4 = a+6d

a+6d=-4...........(1)

similarly, tn = a+(n-1)d

t13 = a+(13-1)d

-16 = a+12d

a+12d = -16..........(2)

subtracting eq (1) from (2),

6d = -12

d = -2

substituting, d= 2 in eq (1),

a + 6(-2) = -4

a - 12 = -4

a = -4 +12

a = 8

a = -26 & d = 2

t1 = a = 8

t2 = t1 + d

= 8 + (-2)

t2 = 6

t3 = t2 + d = 6 - 2 = 4

t4 = t3 + d = 4 - 2 = 2

The sequence of A.P is 8,6,4,2,.........