MATH SOLVE

4 months ago

Q:
# given that a1=5 and a2=15 are the first two terms of a geometric sequence, determine the values of a3 and a10. Show the calculations that lead to your answer

Accepted Solution

A:

a_3 is 45 and a_10 is 98415Step-by-step explanation:Givena_1 = 5a_2 = 15First of all we have to calculate the common ratio of the sequence. The common ratio is the ratio between two consecutive terms of a geometric sequence.So,[tex]r=\frac{a_2}{a_1} = \frac{15}{5} = 3[/tex]The explicit formula for geometric sequence is:[tex]a_n = a_1.r^{n-1}[/tex]Putting the value of r and a_1[tex]a_n = 5.(3)^{n-1}[/tex]Putting n=3 in the explicit formula[tex]a_3 =5.3^{3-1}\\= 5 * 3^2\\=5 * 9\\= 45[/tex]Putting n=10 for tenth term[tex]a_{10} =5.3^{10-1}\\=5*3^9\\=5 * 19683\\=98415[/tex]Hence,a_3 is 45 and a_10 is 98415Keywords: Geometric sequence, Explicit formulaLearn more about geometric sequence at:brainly.com/question/10978510brainly.com/question/11007026#LearnwithBrainly