Question

In an arthimetic progression,
a6= -11
a11= -146
a15= ?​

Answer 1

$- 11 = a + (6 - 1)d \\ - 11 = a + 5d - - - eq1 \\ \\ - 146 = a + (11 - 1)d \\ - 146 = a + 10d - - - eq2\\ \\ subtract \: eq1 \: from \: eq2 \: we \: get \\ - 135 = 5d \\ \frac{ - 135}{5} = d \\ 27 = d \\ \\ by \: putting \: d \: in \: eq1 \: we \: get \\ a = - 146 \\ \\ {a}^{15} = - 146 + (15 - 1)27 \\ {a}^{15} = - 146 + 378 \\ {a}^{15} = 232$