Question

Show work and explain with formulas.

Find the first four terms of the sequence if a_1 = 9, a_n = 5(a_n-1) - 7​

Answer 1

`\large\boxed{a_1=9,\ a_2=38,\ a_3=183,\ a_4=908}`

Explanation:

We have the sequence in recursive formula:

`\left\{\begin{array}{ccc}a_1=99\\a_n=5(a_(n-1))-7\end{array}\right`

Therefore

`a_2=5a_(2-1)-7=5a_1-7\to a_2=5(9)-7=45-7=38\\\\a_3=5a_(3-1)-7=5a_2-7\to a_3=5(38)-7=190-7=183\\\\a_4=5a_(4-1)-7=5a_3-7\to a_4=5(183)-7=915-7=908`

Answer 2

Answer:
`\bold{a_1=9\qquad a_2=38\qquad a_3=183\qquad a_4=908}`

Explanation:

`a_1=9\qquad a_n=5(a_(n-1))-7\\\\a_2=5(a_1)-7\\.\quad =5(9)-7\\.\quad =45-7\\.\quad =\large\boxed{38}\\\\\\a_3=5(a_2)-7\\.\quad =5(38)-7\\.\quad =190-7\\.\quad =\large\boxed{183}\\\\\\a_4=5(a_3)-7\\.\quad =5(183)-7\\.\quad =915-7\\.\quad =\large\boxed{908}`