Question

If the 10th term of an A.P. is 52 and the 17th term is 20 more than the 13th term, Find the A.P.​

Answer 1

Step-by-step explanation:

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Answer 2

Answer :

$\large{\star\:\:\boxed{\bf{A.P.\:\: :-\:7\:,\:12\:,\:17\:,...}}\:\:\star}$

Explanation :

Given :–

• a₁₀ = 52
• a₁₇ = a₁₃ + 20

To Find :–

• Sequence of the A.P. (Arithmetic Progression)

Formula Applied :–

• $\boxed{\bf{\star\:\:a_n\:=\:a\:+\:(n\:-\:1)d\:\:\star}}$

Solution :–

We have ,

$\rightarrow\sf{a_{10}\:=\:52}$

$\rightarrow\sf{a_{10}\:=\:a\:+\:(10\:-\:1)d}$

$\rightarrow\sf{52\:=\:a\:+\:9d}\:\:-----\:\bf{(1)}$

We also know that :

$\rightarrow\sf{a_{17}\:=\:a_{13}\:+\:20}$

$\rightarrow\sf{[a\:+\:(17\:-\:1)d]\:=\:[a\:+\:(13\:-\:1)d]\:+\:20}$

$\rightarrow\sf{a\:+\:16d\:=\:a\:+\:12d\:+\:20}$

$\rightarrow\sf{a\:-\:a\:+\:16d\:-\:12d\:=\:20}$

$\rightarrow\sf{4d\:=\:20}$

$\rightarrow\sf{d\:=\:\dfrac{20}{4} }$

$\rightarrow\boxed{\bf{d\:=\:5} }$

Putting this value of 'd' in Equation(1) :-

$\rightarrow\sf{52\:=\:a\:+\:9(5)}$

$\rightarrow\sf{52\:=\:a\:+\:45}$

$\rightarrow\sf{a\:=\:52\:-\:45}$

$\rightarrow\boxed{\bf{a\:=\:7}}$

Now we will find terms of the A.P.  :-

☆ First Term :-

⇒ a₁ = 7

☆ Second Term :-

⇒ a₂ = a + (2 - 1)d

⇒ a₂ = 7 + 5

⇒ a₂ = 12

☆ Third Term :-

⇒ a₃ = a + (3 - 1)d

⇒ a₃ = 7 + 2(5)

⇒ a₃ = 7 + 10

⇒ a₃ = 17

∴ The sequence of the A.P. will be 7 , 12 , 17 ,...