Question

The 4th term of an A.P is 24 and its 7th term is 36. Find Find the AP? ​

Answer 1

Step-by-step explanation:

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Answer 2

Given :

• 4th term of the AP is 24
• 7th term of the AP is 36

　

To Find :

• The AP

　

Solution :

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$\sf{a_{4}= 24 ~ \implies a+3d=24}$ ______(1)

$\sf{a_{7}= 36 ~ \implies a+6d=36}$ ______(2)

　

• (2) – (1)

$\sf{~~~~~~~~~~ (a+6d) - (a+3d) = 36 - 24}$

$\sf\implies{{\cancel{~a}}+6d~{\cancel{-a}}-3d=12}$

$\sf\implies{3d = 12}$

$\sf\implies{d={\dfrac{12}{3}}}$

$\sf\implies{d={\pmb{4}}}$

• Common Difference, D = 4

$\sf{~~~~~~~~~~ a_{4}=a+3d}$

$\sf\implies{24=a+3(4)}$

$\sf\implies{a+3(4)=24}$

$\sf\implies{a+12=24}$

$\sf\implies{a=24-12}$

$\sf\implies{a={\pmb{12}}}$

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∴ Required answer :

　

• $\sf{a={\pmb{12}}}$
• $\sf{a_{2}=a+d=12+4={\pmb{16}}}$
• $\sf{a_{3}=a+2d=12+8={\pmb{20}}}$
• $\sf{a_{4}={\pmb{24}}}$

　

∴ Required AP :

• 12, 16, 20, 24 ...