Question

Find the 12th term of a Gp whose 5th term is 64 and common ratio is common ratio is 2​

Answer 1

Answer:

We know that the formula for the nth term of an G.P is T

n

=ar

n−1

, where a is the first term, r is the common ratio.

It is given that the fifth term of G.P is T

5

=64 and the common ratio is r=2, therefore,

T

n

=ar

n−1

⇒T

5

=a×(2)

5−1

⇒64=a×(2)

4

⇒64=16a

⇒a=

16

64

=4

Now we have the first term a=4 and the common ratio r=2, thus,

T

12

=4×(2)

12−1

=4×(2)

11

=4×2048=8192

Hence, T

12

=8192.

Answer 2

$\sf{\underline{\underline{\pink{Question}}}}$

Find the 12th term of a Gp whose 5th term is 64 and common ratio is common ratio is 2.

$\sf{\underline{\underline{\pink{Given}}}}$

• 5th term $(a_5)=64$
• common ratio = 2

$\sf{\underline{\underline{\pink{To\:Find}}}}$

• 12th term =?

$\sf{\underline{\underline{\pink{Solution}}}}$

• Finding 1st term of a G.P

$\sf→ a_5=64\\\sf→ ar^{n-1}=64\\\sf→ a×2^{5-1}=64\\\sf→ a×2^4=64\\\sf→ 16a=64\\\sf→ a=\frac{64}{16}\\\sf{\red{\fbox{\underline{a=4}}}}$

Now,

• Finding 12th term of a G.P

$\sf→ a_{n}=ar^{n-1}\\\sf→ a_{12}=4×2{12-1}\\\sf→ a_{12}= 4×2{11}\\\sf→ a_{12}= 4×2048\\\sf{\fbox{\red{\underline{a_{12}=8192}}}}$