Question

Which term of the AP -7 , -12 , -17, -22 will be -82 ? Is -100 any term of the AP ? Give reasons ?

Answer 1

a=-7 d=-5 an=-82
an=a+(n-1)d
-82= -7+(n-1)(-5)
-75=(n-1)(-5)
75/5=(n-1)
15=(n-1)
n=16th term is -82.

an=-100
-100=-7+(n-1)(-5)
-93=(n-1)(-5)
93/5=(n-1)
*since n is a natural number therefore it will not be in fraction. Hence -100 is not the term of this
A.P.

hope it helps ☺️☺️

Answer 2

Answer:

The final answer is

1) -82 is part of the AP

2) -100 is not part of the AP

Step-by-step explanation:

AP is arithmetic progression. It is basically a sequence of numbers where an initial number is added with another number and this same process continues throughout.

Given,

a1 = -7

a2 = -12

a2 - a1 = d

           =  -12 - (- 7)

           = - 5

an = -82

d = 5

a = -7

an = a+ (n-1)d

If there exists a whole value n, then -82 is a part of the progression.

-82 = -7 + (n-1)*-5

-82+7 = (n-1)*-5

-75/-5 = n-1

25 = n-1

n = 26

Hence 82 is a part of the progression.

-100 = -7 + (n-1)*-5

93/5 = n-1

n will not be a whole number hence, -100 is not part of the Progression.

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