Answer:
The first term is 128
Step-by-step explanation:
The common ratio of the geometric series is given as:
[tex]r = \frac{1}{4} [/tex]
The sum of the first 4 term is 170.
The sum of first n terms of a geometric sequence is given b;
[tex]s_n=\frac{a_1(1-r^n)}{1-r}[/tex]
We put the common ratio, n=4 and equate to 170.
[tex]\frac{a_1(1-( \frac{1}{4} )^4)}{1- \frac{1}{4} } = 170[/tex]
Simplify:
[tex]\frac{a_1(1- \frac{1}{256} )}{ \frac{3}{4} } = 170[/tex]
[tex] \frac{255}{256} a_1 = \frac{3}{4} \times 170[/tex]
[tex]\frac{255}{256} a_1 = \frac{255}{2} [/tex]
[tex]\frac{1}{256} a_1 = \frac{1}{2} [/tex]
[tex] a_1 = \frac{1}{2} \times 256[/tex]
[tex]a_1 = \frac{1}{2} \times 256 = 128[/tex]
