Question

The 10th term of an a.p is -27 and the 5th term is -12 .find the first term?​

Answer 1

Step-by-step explanation:

$a_{10} = - 27... (Given) \\\\\therefore a + 9d = - 27...... (1)\\\\a_{5} = - 12... (Given) \\\\\therefore a + 4d = - 12.......(2)$

Subtracting equation (2) from equation (1)

$a + 9d-( a + 4d )= - 27-(-12)\\\\\therefore a +9d - a-4d = - 27+12\\\\\therefore 5d = - 15\\\\\therefore d = \frac {- 15}{5}\\\\\huge \orange {\boxed {\therefore d = -3}}$

Substituting d = - 3 in equation (1), we find:

$a + 9\times (-3)= - 27\\\\\therefore a - 27 = - 27\\\\\therefore a = 27- 27\\\\\huge \red {\boxed {\therefore a = 0}}$

Hence, first term is zero.