If the 6th term of the sequence is 60 and the common ratio is 2 find the first term​

SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & n = 6 \\ & a_6 = 60 \\ & r = 2 \end{aligned}[/tex]Step 2: Solve for the 1st term of a geometric sequence.[tex]\begin{aligned} a_n & = a_1r^{n - 1} \\ a_6 & = a_1(2)^{6 - 1} \\ 60 & = a_1(2)^5 \\ 60 & = 32a_1 \\ 32a_1 & = 60 \\ \frac{32a_1}{32} & = \frac{60}{32} \\ a_1 & = \boxed{\frac{15}{8}} \end{aligned}[/tex]Hence, the 1st term of a geometric sequence is 15/8.

Answered by GreatRedSpot | 2024-09-02