## the 7th term of ap is -4 and its 13 term is -16 find the ap

Question

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

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2 months 2021-11-28T15:45:05+00:00 2 Answers 0 views 0

a=8

d=(-2)

The formula for nth term is,

an=a+(n-1)d

Hence substituting 7 in the place of n, we get,

a7=a(7-1) d

a7=a+6d…… (eq-1)

Similarly, Substituting 13 in the place of n, we get,

a13=a+(13-1)d

a13=a+12d…… (eq-2)

Subtracting Equation (2) from (1), we get,

-6d=12,

d=12/-6

d=-2

Hence substituting d=-2 in any of the equations

we get,

a=8

Hence the A. P is,

8,6,4,2,0,-2, -4, -6…..

## Step-by-step explanation:

given that

7th term is -4,so

a +6d =-4 let this be equation 1

and

a +12d = 13 let this be equation 2

adding equation 1 and 2 we get

## 2a + 18d  = -20

dividing the equation by 2 we get

a +9d =-10

therefore the 8th term is -10

d = 8th term -7th term

d= -10 +4

d= -6

substituting in eq 1 we get

a+6(-6) =-4

a-36=-4

a= 32

a+d = 32-6=26

a+2d = 32-12 =20

a+3d =32-18= 14

therefore the AP is 32,26,20.14……….