If the $6^{\text {th }}$ term of an A.P. is equal to four times its first term and the sum of first six terms is 75, find the first term and the common difference.
The $2^{\text {nd }}$ and $45^{\text {th }}$ term of an arithmetic progression are 10 and 96 respectively. Find the first term and the common difference and hence find the sum of the first 15 terms.