Question

In An A.S 1, 6, 11 find the common difference find 20th term

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Answer 1

To Find :

• we need to find the common difference.
• 20th term of AP.

Given :

• A P = 1 ,6 ,11 ...

Solution :

• AP = 1 , 6 ,11
• First term (a) = 1

Common difference (d) = a2 - a1

• a2 = 6
• a1 = 1

⟹ d = 6 - 1

⟹ d = 5

Now,

• a3 - a2
• a3 = 11
• a2 = 6

⟹ d = 11 - 6

⟹ d = 5

So,

• Common difference (d) = 5

Now,

• Finding 20th term of Given AP :-

we know that,

• an = a + (n - 1)d

⟹ a20 = 1 + (20 - 1)5

⟹ a20 = 1 + 19 × 5

⟹ a20 = 1 + 95

⟹ a20 = 96

Hence,

• Common difference (d) = 5
• 20th term of AP = 96

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Answer 2

$\rm\huge\blue{\underline{\underline{\underline{ Question : }}}}$

In an AP : 1,6,11..... find the common difference (d) & 20th term of AP.

$\rm\huge\blue{\underline{\underline{\underline{ Solution : }}}}$

★ Given that,

• AP : 1,6,11.....

★ To find,

• Common difference. (d)
• 20th term of AP.

★ Let,

• a1 = 1
• a2 = 6
• a3 = 11

↪ Common difference = a2 - a1

$\sf\green{:\implies a_{2} - a_{1}}$

$\sf\:\implies 6 - 1$

$\sf\:\implies 5$

$\sf\green{ :\implies a_{3} - a_{1} }$

$\sf\:\implies 11 - 6$

$\sf\:\implies 5$

✒ From the above we can see that the difference between the successive terms is same (constant) which is 5.

✒ So we can say that the given sequence is in A.P.

✒ If the 1st term and the common difference 'd' is given then we can make an arithmetic sequence.

$\boxed{\therefore common \: difference = 5}$

★ Now,

To find the value of 20th term.

$\sf\:\implies a_{20} = a + 19d$

• a = 1
• d = 5

$\sf\:\implies a_{20} = 1 + 19(5)$

$\sf\:\implies 1 + 95$

$\sf\:\implies 96$

$\underline{\boxed{\bf{\purple{ \therefore Common\:difference(d) = 5,20^{th} \: term = 96}}}}\:\orange{\bigstar}$

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★ Important formulas in AP :

$\rm\red{ : \implies a_{n} = a + (n - 1)d }$

$\rm\red{ : \implies S_{n} = \frac{n}{2} [ 2a + (n - 1)d ] }$

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