The first term of a g. P is 15 and the common ratio is 2 find the 12th term and the sum of the first 9 term
Answers
EXPLANATION.
First term of a G. p = 15 = a
common ratio of Gp = r = 2
Find 12th term and the sum of first 9th
term.
According to the question,
Formula of Nth term of an Gp
=> 12 th term of an Gp
=> 12 th term = 30,720
Formula of sum of Nth term of an Gp
=> S9 = 15 X 511
=> S9 = 7665
Therefore,
12th term = 30720
sum of 9th term = 7665
Step-by-step explanation:
EXPLANATION.
First term of a G. p = 15 = a
common ratio of Gp = r = 2
Find 12th term and the sum of first 9th
term.
According to the question,
Formula of Nth term of an Gp
\boxed{\bold{ \implies{t_{n} = ar {}^{(n \: - \: 1)} }}}
⟹t
n
=ar
(n−1)
=> 12 th term of an Gp
12th \: \: \: term \: \: = ar {}^{11} = 15(2) {}^{11}12thterm=ar
11
=15(2)
11
=> 12 th term = 30,720
Formula of sum of Nth term of an Gp
\boxed{\bold{ \implies{s_{n} \: = \frac{a(r {}^{n \: } - 1) }{(r \: - 1)}} }}
⟹s
n
=
(r−1)
a(r
n
−1)
\boxed{\implies{\bold{s_{9} \: = \frac{15(2 {}^{9} - 1) }{(2 \: - 1)}} }}
⟹s
9
=
(2−1)
15(2
9
−1)
\implies{ s_{9} \: = 15(512 \: - 1) }⟹s
9
=15(512−1)
=> S9 = 15 X 511
=> S9 = 7665
Therefore,
12th term = 30720
sum of 9th term = 7665