Question

The 7th term of an AP is 15 and the fourth is 9. Find the sequence, first term and the common difference

Answer 1

The common difference could be find according to formula

$$d=\frac{a_{m}-a_{n}}{m-n}=\frac{a_{7}-a_{4}}{7-4}=\frac{15-9}{7-4}=\frac{6}{3}=2$$

Any term of arithmetic progression is

$$a_{n}=a_{1}+(n-1)d$$

From here the first term is

$$a_{1}=a_{n}-(n-1)d=a_{4}-(4-1)\cdot d=9-(4-1)\cdot 2=3$$

Answer: the first term a₁=3 and the common difference d=2.