Question

Which term of the A.P. –7, –12, –17, –22,... will be –82? Is –100 any term of the A.P.?

Answer 1

Given: The A.P. is –7, –12, –17, –22,... so a = –7, d = –5.

nth term formula: a_n = a + (n – 1)d

Substitute a and d: a_n = –7 + (n – 1)(–5)

= –7 – 5(n – 1) 

= –2 – 5n

For a_n = –82:

–2 – 5n = –82

–5n = –80

n = 16

For a_n = –100: 

–2 – 5n = –100

–5n = –98 

n = 19.6 (not a natural number)

–82 is the 16th term of the A.P.; –100 is not any term of this A.P.