Question

find the 10th term of 512 256 128​

Answer 1

Answer:

a=512,d=a2-a1=256-512=-256

Step-by-step explanation:

a10=a+9d

a10=512+9(-256)

a10=-1792

Answer 2

The 10th term of 512 256 128​ is 1

Step-by-step explanation:

• Given that

        Series 512, 256, 128, . . .

• Here we see that

        ​$\mathbf{\textrm{First term }(a_{1})=512}$

        $\mathbf{\textrm{Second term }(a_{2})=256}$

        $\mathbf{\textrm{Third term }(a_{3})=128}$

• Ratio of second term to first term is

        $\mathbf{\frac{a_{2}}{a_{1}}=\frac{256}{512}=0.5}$

• Similarly ratio of third term to second term is

        $\mathbf{\frac{a_{3}}{a_{2}}=\frac{128}{256}=0.5}$

• From here we see that ratio of two consecutive term is constant. So it is in G.P series. Where common ratio is 0.5.

• So common ratio (r) = 0.5

• We know the formula of nth term

        $\mathbf{T_{n}=ar^{n-1}}$

• Then 10th term of G.P series can be obtain by putting

       a =512  and r = 0.5

        $\mathbf{T_{10}=512\times 0.5^{10-1}}$

        $\mathbf{T_{10}=2^{9}\times 0.5^{9}}$

        It can be written as

       $\mathbf{T_{10}=(2\times 0.5)^{9}=1^{9}=1}$