Question

Which term of the ap -7,-12,-17,-22... Will be -82? Is -100 any term of the ap? Give reason for your answer

Answer 1

A.P. Formula

→ aₙ = a + (n - 1)d

• aₙ = value of any term
• a stands for first term
• d stands for comman difference
• n stands for placing in a term

So if value of aₙ is 82 then,

→ - 82 = - 7 + (n - 1)(- 5)

→ - 75 = 5 - 5n

→ - 80 = - 5n

→ 16 = n

Hence 16th term of A.P. will be - 82.

Verification

[If - 100 is any term in A.P]

→ - 100 = - 7 + (n - 1)(- 5)

→ - 93 = 5 - 5n

→ 98/5 = n

Since term nth can't be in fraction therefore - 100 is not term in A.P.

Answer 2

The given A.P. is -7,-12,-17,-22....

First term (a) = -7

Common difference (d) = -12 - (-7) = -5

Let nth term of A.P. be -82.

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

-75 = (n-1)(-5)

n-1 = 15

n = 15+1

n = 16

So, -82 is the 16th term of A.P.

Let pth term of A.P. be -100.

-100 = -7 + (p-1) (-5)

-93 = (p-1)(-5)

p-1 = 93/5

p = 93/5 + 1

p = 98/5

So, -100 is not the term of A.P.