Question

Given the geometric sequence defined by the following values of aa0 and ????????, find the value of nn so that aann has the

specified value.
a0 = 6.7, ???? = 1.9, an = 7804.8

Answer 1

11

Explanation:

The first term of the geometric sequence is given to be a₀, the common ratio r and the (n+1)th term is aₙ.

Now, the condition is given a₀ =6.7, r=1.9 and aₙ=7804.8.

Therefore, a₀.rⁿ=7804.8 = aₙ

⇒ 6.7(1.9)ⁿ=7804.8

⇒(1.9)ⁿ =1164.89

Now, taking log both sides we get,

⇒n log (1.9) =log (1164.89)

⇒n =log (1164.89)/log(1.9) =10.9999≈11

Therefore, the value of n is 11.