Question

The second term of arithimetic sequence is 38 and sixth term of arithimetic sequence is 22 find the 5th term?​

Answer 1

Answer:

a+n=38

a+ 5n=22

so a and a gets cancelled

so 4n= -16

n=-4

so substituting n=-4 in a+n=38

a=42

so the fifth term will be

a+4n=42+(-4×4)=42-16= 26

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Answer 2

Answer:

$\bigstar{\bold{Fifth\:term\:of\:AP\:is\:26}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Second term of AP(a₂) = 38
• Sixth term of AP(a₆) = 22

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Fifth term of AP(a₅)

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ The common difference of the AP is given by the equation

   $d=\frac{a_m-a_n}{m-n}$

  where $a_m=a_6=22$, $a_n=a_2=38$, $m=6$, $n=2$

→ Substituting the give datas, we get

   $d=\frac{22-38}{6-2}$

   $d=\:-4$

→ The fifth term of the AP can be found out by

   a₅ = a₆-d

→ Substituting the datas we get

   a₅ = 22+4

   a₅ = 26

  $\boxed{\bold{The\:fifth\:term\:of\:AP\:is\:26}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

• The common difference of an AP is the difference between its two consecutive terms.
• It can be found out by the following formulae:

• $d=\frac{a_m-a_n}{m-n}$

• $d=a_2-a_1$