MATH SOLVE

4 months ago

Q:
# Get the general term for the sequence being your t3 = 11 and the t20 = 244.2

Accepted Solution

A:

Answer:nth term = [tex]t_{n} = 7.639(1.2)^{n - 1}[/tex]Step-by-step explanation:Let us assume that the given sequence is a G.P.
Now, if the first term of the G.P. is a and the common ratio is r, then
Third term = [tex]t_{3} = ar^{2} = 11[/tex] .......... (1) and 20th term = [tex]t_{20} = ar^{19} = 244.2[/tex] ........... (2)
Now, dividing equation (2) with equation (1) we get
[tex]\frac{ar^{19} }{ar^{2} } = \frac{244.2}{11} = 22.2[/tex]
⇒ [tex]r^{17} = 22.2[/tex]
⇒ r = 1.2.
Hence, from equation (1) we get
a(1.2)² = 11
⇒ a = 7.639 (Approx.)
Therefore, the general term of the sequence i.e. nth term = [tex]t_{n} = 7.639(1.2)^{n - 1}[/tex] (Answer)