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

Step-by-step explanation:

Given: AP:-7, -12, -17, -22.

Here, a=-7,

d=a2-a=-12-(-7)

=>-12+7

d=-5.

Formula:

$l = a + (n - 1) \times d$

(I). Last term, l=-82

=> -82=-7+(n-1)×(-5)

=>™-82+7=(n-1)×(-5)

=> -75/-5=n-1

=> 15+1=n.

=> 16=n

: -82 is the 16th term of the given AP.

(ii).Any term= -100.

=> -100=-7+(n-1)×(-5)

=>-100=-7-5n+5

=> -100=-2+5n

=> -100+2=5n

=> -98/5=n.

=> n cannot be fraction.

: No, -100 is not any term of the given AP.