Question

In an AP 12th term is -13 and the sum of the first four terms is 24.find first term 'a' and common difference 'd'

Answer 1

Step-by-step explanation:

Given:

$t_{12}= - 13 \\ \implies \: a + (12 - 1)d = - 13 \\ \implies \: a + 11d = - 13 \\ \implies \: a = - 13 - 11d....(1) \\ next \\ s_{4}= 24 \\ \implies \: \frac{4}{2} \{2a + (4 - 1)d \} = 24 \\ \implies \: 2 \{2a + 3d \} = 24 \\ \implies \: 2a + 3d = 12 ....(2)\\ from \: equations \: (1) \: and \: (2) \: we \: find : \\ 2( - 13 - 11d) + 3d = 12 \\ \implies \: - 26 - 22d + 3d = 12 \\ \implies \: - 19d = 12 + 26 \\ \implies \: - 19d = 38 \\ \implies \: d = \frac{38}{ - 19} \\ \implies \: \huge \fbox{ d = - 2} \\ from \: equation \: (1) \\ a = - 13 - 11( - 2) = - 13 + 22 = 9 \\ thus \: \: \: \huge \fbox{a = 9}$