Question

6. If 18 th and 11 th term of an AP are in the ratio of 3:2, then its 21 st and 5 th terms are in ratio of

Answer 1

Answer:

3:1 is the required ratio for the given problem

Answer 2

Answer:-

$\sf{The \ ratio \ of \ 21^{st} \ and \ 5^{th} \ term \ of}$

$\sf{the \ AP \ is \ 3:1.}$

Given:

• If 18 th and 11 th term of an AP are in the ratio of 3:2.

To find:

• Ratio of it's $\sf{21^{st} \ and \ 5^{th} \ term}$

Solution:

$\boxed{\sf{t_{n}=a+(n-1)d}}$

$\sf{According \ to \ the \ given \ condition. }$

$\sf{\frac{t_{18}}{t_{11}}=\frac{3}{2}}$

$\sf{\therefore{\frac{a+17d}{a+10d}=\frac{3}{2}}}$

$\sf{\therefore{2(a+17d)=3(a+10d)}}$

$\sf{\therefore{2a+34d=3a+30d}}$

$\sf{\therefore{3a-2a=34d-30d}}$

$\boxed{\sf{\therefore{a=4d}}}$

$\sf{\frac{t_{21}}{t_{5}}=\frac{a+20d}{a+4d}}$

$\sf{But, \ a=4d}$

$\sf{\therefore{\frac{t_{21}}{t_{5}}=\frac{4d+20d}{4d+4d}}}$

$\sf{\therefore{\frac{t_{21}}{t_{5}}=\frac{24d}{8d}}}$

$\sf{\therefore{\frac{t_{21}}{t_{5}}=\frac{3}{1}}}$

$\sf\purple{\tt{\therefore{The \ ratio \ of \ 21^{st} \ and \ 5^{th} \ term \ of}}}$

$\sf\purple{\tt{the \ AP \ is \ 3:1.}}$