Question

here are the first 3 terms of a different sequence 1,2,4 write down two numbers that could be 4th term and the 5th term of this sequence

Answer 1

Answer:

$\sf{The \ 4^{th} \ and \ 5^{th} \ term \ are}$

$\sf{8 \ and \ 16 \ respectively.}$

Given:

$\sf{The \ given \ sequence \ is \ 1, \ 2, \ 4,...}$

To find:

$\sf{The \ 4^{th} \ and \ 5^{th} \ term \ of \ the \ sequence}$

Solution:

$\sf{Here, \ t_{1}=1,} \ t_{2}=2 \ and \ t_{3}=4$

$\sf{Now,}$

$\sf{\dfrac{t_{2}}{t_{1}}=\dfrac{2}{1}=2}$

$\sf{Also,}$

$\sf{\dfrac{t_{3}}{t_{2}}=\dfrac{4}{2}=2}$

$\sf{Hence, \ the \ given \ sequence \ is \ an \ G.P.}$

$\sf{Here, \ a=1 \ and \ r=2}$

$\boxed{\sf{a_{n}=ar^{n-1}}}$

$\sf{\therefore{a_{4}=1(2)^{4-1}}}$

$\sf{\therefore{a_{4}=2^{3}}}$

$\sf{\therefore{a_{4}=8}}$

$\sf{a_{5}=1(2)^{5-1}}$

$\sf{\therefore{a_{5}=2^{4}}}$

$\sf{\therefore{a_{5}=16}}$

$\sf\purple{\tt{\therefore{The \ 4^{th} \ and \ 5^{th} \ term \ are}}}$

$\sf\purple{\tt{8 \ and \ 16 \ respectively.}}$

_____________________________

$\sf\blue{Extra \ information:}$

$\sf{In \ a \ G.P. \ sum \ of \ n \ terms}$

$\sf{is \ given \ by}$

$\sf{S_{n}=a\times\dfrac{(r^{n}-1)}{(r-1)}}$