Question

Give the first four terms of the geometric sequence for which A1 = -7 and r = -4.07 7 7 74, 16, 64, 256 -7,28, -112, 448 -7, -11, -15, -1928. -112, 448. - 1792

Answer 1

Given:

`\begin{gathered} firstterm(a_1\text{) = -7} \\ \text{common ratio (r) = -4} \end{gathered}`

Required: First four terms

The nth term of a geometric sequence :

`a_{n\text{ }}=a_1\text{ }* r^(n-1)`

Hence, we can obtain the next four terms by substituting

`\begin{gathered} \text{when n = 1, a}_1\text{ = -7} \\ n=2,a_2\text{ =-7 }*(-4)^{2\text{ - 1}} \\ a_2\text{ = -7 }*\text{ -4} \\ =\text{ 28} \\ \\ \text{when n =3, a}_3\text{ = -7 }*(-4)^{3\text{ -1 }} \\ a_3\text{ = -7 }*\text{ 16} \\ =\text{ -112} \\ \\ \text{when n = 4, a}_4\text{ = }-7\text{ }*(-4)^(4-1) \\ a_4\text{ = -7 }*\text{ -64} \\ =\text{ 448} \end{gathered}`