Question

7th term of an ap is -4 and its 13 th term is -16.find the ap. ​

Answer 1

Here is your solution

mistake in ques it should be 62 instead of 72

a+6d=32, .............. (1)

a+12d=62................... (2)

on subtracting equation 1 from. ii

a+12d-a-6d=62-32

6d= 30

d=5

hence, a=2

Ap are 2,2+5,2+5+5,2+5+5+5

Ap are 2,7,12,17

hope it helps you

Answer 2

General term of AP is Tn=a + (n-1)d

where a is first term and d is common difference

7th term T7=-4=a+(7-1)d=a+6d

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

13th term T13=-16=a+(13-1)d

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

solving the equations

multiplying equation 1 with 2 it becomes

2a+12d=-8

subtracting (2) from above equation

2a+12d -(a+12d)=-8-(-16)

a=-8+16

a=8

substitute a=8 in (1)

a+6d=-4

8+6d=-4

6d=-12

d=-2

The series is

a,a+d,a+2d,a+3d,..............,a+(n-1)d

8,6,4,2,0,-2,-4,-6...........,8+(n-1)(-2)