Question

Which term of an A.P :
18,15,12,........... is -75​

Answer 1

$\mathrm \green{ a_{1} = 18 }$

$\mathrm \green{d = a_{2} - a_{1} }$

$\mathrm \green{d = 15 - 18 = - 3}$

$\mathrm \green{a_{n} = - 75 }$

we know that,

$\mathrm \blue{a_{n} = a + (n - 1)d}$

so, fill all values in the above formula.

$\mathrm{ - 75 = 18 + (n - 1)( - 3)}$

$\tt{ - 75 = 18 - 3n + 3}$

$\tt{ - 75 = 21 - 3n}$

$\tt{ - 75 - 21 = - 3n}$

$\tt{ - 3n = - 96}$

Minus minus will get cancelled.

$\tt{n = \frac{96}{3} }$

$\tt \purple{ \boxed{ \boxed{n =32 }}}$

Hope my answer will help you.