Question

if t54 of an A.P. is -61 and t4=64, find t10

Answer 1

$tn = a + (n - 1)d \\ t54 = a + (54 - 1)d = - 61 \\ a + 53d = - 61 \\ similarly \: t4 = a + 3d = 64 \\ a + 53d = - 61 \\ a + 3d = 64 \\ from \: subtraction \\ 50d = - 125 \\ d = - 5 \div 2 \\ a = 143 \div 2 \\ t10 = a + 9d \\ \: \: \: \: \: = (143 \div 2) \: + 9( - 5 \div 2) \\ \: \: \: \: = 98 \div 2 \\ \: \: \: = 49$