Question

If the first term of an ap is 8 , nth term is 33 and sum is 133

Answer 1

$First\: term , a_{1} = 8 \\ nth \:\:term\:of \:AP,a_{n} = 33 \\ a+(n-1)d = 33 \\ 8+(n-1)d = 33 \\ (n-1)d = 33-8 \\ (n-1)d = 25 \\\\ Sum\: of \:n \:terms,S_{n} = 123 \\ \frac{n}{2} [a+a+(n-1)d] = 123 \\ n[8+33] = 123(2) \\ n[41] = 246 \\ n = 246/41 \\ n = 6 \\\\ (n-1)d = 25 \\ (6-1)d = 25 \\ 5d = 25 \\ d = 25/5 \\ d = 5$