Question

fie an o progresie geometrica cu ratia 2 . daca termenilor a1,a4,a6 li se adauga 18 34 respectiv 16 ,numerele obtinute sunt in progresie aritmetica sa se determine progresia an

Answer 1

   
[tex]\displaystyle \bf\\ a_1;~a_4;~a_6 ~~~\text{\bf apartin unei progresii geometice cu ratia 2.}\\\\ a_4 = 2^3a_1 = 8a_1\\ a_6 = 2^5 a_1 = 32a_1\\\\ a_1+18;~~8a_1+34;~~32a_1+16~~~~\text{\bf sunt in progresie aritmetica.}\\\\ \frac{a_1+18 + 32a_1+16}{2} = 8a_1+34\\\\ \frac{33a_1+34}{2} = 8a_1+34\\\\ 33a_1+34 = 2(8a_1+34)\\\\ 33a_1+34 = 16a_1+68\\\\ 33a_1 -16a_1 =68-34\\\\ 17a_1=34\\\\ a_1 = \frac{34}{17} \\\\ \boxed{\bf a_1 =2}~si~\boxed{\bf q =2} [/tex]