Question

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

Answer is 0 ​

Answer 1

⇝ 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,

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

Answer 2

Given :-

The 17th term of an arithmetic sequence is 5 and 5th term is 17.

To Find :-

22nd term

Solution :-

We know that

aₙ = a + (n - 1)d

a₁₇ = a + (17 - 1)d

5 = a + 16d (i)

aₙ = a + (n - 1)d

a₅ = a + (5 - 1)d

17 = a + 4d (ii)

On subtracting them

a + 4d = 17

a + 16d = 5

(-)   (-)  = (-)

-12d = 12

d = -12/12

d = -1

Using 2

17 = a + 4(-1)

17 = a + (-4)

17 + 4 = a

21 = a

Now

aₙ = a + (n - 1)d

a₂₂ = 21 + (22 - 1)(-1)

a₂₂ = 21 + 21(-1)

a₂₂ = 21 - 21

a₂₂ = 0