Question

The 5th term of an arithmetic sequence is 17 and 17th term is 5. what is the 22nd term​

Answer 1

Answer:

22nd term is zero "0"

Step-by-step explanation:

Hope it helped you, plz mark this as brainlliest as i tried for 10 minutes

Answer 2

⇝ Given :-

For An Arthematic Sequence ;

• 5th Term = 17

• 17th term = 5

⇝ To Find :-

• 22nd Term of the corresponding Arthematic Sequence.

⇝ Solution :-

We Know, nth term of an Arthematic Sequence is given by formula :

$\large \bf \red\bigstar \: \: \orange{ \underbrace{ \underline{ a_n = a +(n - 1)d}}}$

where,

• a = First Term

• d = Common Difference

Hence,

❒ According To Question :

$\rm 5th \: term = a_5 = 17$

$:\longmapsto \bf a + 4d = 17 \: - - - (1)$

Also,

$\rm \: 17th \: term \: = a_{17} = 5$

$:\longmapsto \bf a + 16d = 5 \: - - - (2)$

⏩ Subtracting (1) From (2) :

$:\longmapsto \rm 12d = - 12$

$:\longmapsto \rm d = - \cancel \frac{12}{12}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf d = - 1} }}}$

⏩ Putting Value of d in (1) :

$:\longmapsto \rm a + 4 \times ( - 1) = 17$

$:\longmapsto \rm \: a - 4 = 17$

$:\longmapsto \rm a = 17 + 4$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf a =21 } }}}$

Now,

$\rm 22nd \: Term = a_{22}$

$= \rm \: a + 21d$

$= 21 + 21 \times ( - 1)$

$= 21 - 21$

$\green{ \large :\longmapsto  \underline {\boxed{{\bf a_{22} = 0} }}}$

Hence,

$\Large\underline{\pink{\underline{\frak{\pmb{22nd\:\:term = 0 }}}}}$