Question

Is -150 a term of the A.P. 17,12,7,12...?

Answer 1

an =a+(n-1)d

-150=17+(n-1)-5

-150=17-5n+5

-150=22-5n

-150-22=-5n

-172=-5n

n =-172/-5=172/5=34.2

it is not in AP...

Answer 2

Error :- there should be 2 instead of 12 in 4th term!!

$\huge \bf \red{ \mid{ \overline{ \underline{ANSWER}}} \mid}$

$\bf{GIVEN \colon - }$

an = -150

→ a1 = 17

→ a2 = 12

→ a3 = 7 and so on .

let us find common difference

→ d = a2 - a1

→ d = 12-17

→d = -5

→ an = a + (n - 1)d

→ -150 = 17 + (n - 1)5

→ -150 = 17 + 5n - 5

→ -150 = 12 + 5n

→ 5n = -150 - 12

→ 5n = -162

→ n = -162/5

HENCE IT IS NOT THE TERM OF AP