Question

In the 5,8,11,
find the 20th term
​

Answer 1

..Question..

In the given series find the 20ᵗʰ term

➪ 5 , 8 , 11 , ..... nᵗʰ term

..Answer..

Given series :

➪ 5 , 8 , 11 , .............. nᵗʰ term

We are to find :

➪ 20ᵗʰ term of the series

•°• Formula usable :

ㅤㅤ♧︎︎︎ a + ( n - 1 ) d

Where ,

ㅤㅤㅤ➪ a = 5

ㅤㅤㅤ➪ d = 3

ㅤㅤㅤ➪ n = 20

•°• Putting values for 20ᵗʰ term

ㅤㅤㅤ➪ a + ( n - 1 ) d

ㅤㅤㅤ➪ 5 + ( 20 - 1 ) d

ㅤㅤㅤ➪ 5 + ( 20 - 1 ) × 3

ㅤㅤㅤ➪ 5 + ( 19 × 3 )

ㅤㅤㅤ➪ 5 + 57

ㅤㅤㅤ➪ 62

•°• 20ᵗʰ term of the series = 62

_____________________

Let us find the other terms also :

☯︎ 4ᵗʰ term of the series :

ㅤㅤ➪ a + ( n - 1 ) d

ㅤㅤ➪ 5 + ( 4 - 1 ) 3

ㅤㅤ➪ 5 + 3 × 3

ㅤㅤ➪ 5 + 9 = 14

•°• 4ᵗʰ term of the series = 14

Now ,

☯︎ 5ᵗʰ term of the series :

ㅤㅤ➪ a + ( n - 1 ) d

ㅤㅤ➪ 5 + ( 5 - 1 ) 3

ㅤㅤ➪ 5 + 4 × 3

ㅤㅤ➪ 5 + 12 = 17

•°• 5ᵗʰ term of the series = 17

Now ,

☯︎ 6ᵗʰ term of the series :

ㅤㅤ➪ a + ( n - 1 ) d

ㅤㅤ➪ 5 + ( 6 - 1 ) 3

ㅤㅤ➪ 5 + 15 = 20

•°• 6ᵗʰ term of the series = 20

Now ,

☯︎ 7ᵗʰ term of the series :

ㅤㅤ➪ a + ( n - 1 ) d

ㅤㅤ➪ 5 + ( 7 - 1 ) 3

ㅤㅤ➪ 5 + 18 = 23

•°• 7ᵗʰ term of the series = 23

Now ,

☯︎ 8ᵗʰ term of the series :

ㅤㅤ➪ a + ( n - 1 ) d

ㅤㅤ➪ 5 + ( 8 - 1 ) 3

ㅤㅤ➪ 5 + 21 = 26

•°• 8ᵗʰ term of the series = 26

Now ,

☯︎ 9ᵗʰ term of the series :

ㅤㅤ➪ a + 8d

ㅤㅤ➪ 5 + 8 × 3

ㅤㅤ➪ 29

•°• 9ᵗʰ term of the series = 29

Now ,

☯︎ 10ᵗʰ term of the series :

ㅤㅤ➪ a + 9d

ㅤㅤ➪ 5 + 9 × 3

ㅤㅤ➪ 32

•°• 9ᵗʰ term of the series = 32

Now ,

☯︎ 11ᵗʰ term of the series :

ㅤㅤ➪ a + 10d

ㅤㅤ➪ 5 + 10 × 3

ㅤㅤ➪ 35

•°• 11ᵗʰ term of the series = 35

Now ,

☯︎ 12ᵗʰ term of the series :

ㅤㅤ➪ a + 11d

ㅤㅤ➪ 5 + 11 × 3

ㅤㅤ➪ 38

•°• 12ᵗʰ term of the series = 38

Now ,

☯︎ 13ᵗʰ term of the series :

ㅤㅤ➪ a + 12d

ㅤㅤ➪ 5 + 12 × 3

ㅤㅤ➪ 41

•°• 13ᵗʰ term of the series = 41

Now ,

☯︎ 14ᵗʰ term of the series :

ㅤㅤ➪ a + 13d

ㅤㅤ➪ 5 + 13 × 3

ㅤㅤ➪ 44

•°• 14ᵗʰ term of the series = 44

Now

☯︎ 15ᵗʰ term of the series :

ㅤㅤ➪ a + 14d

ㅤㅤ➪ 5 + 14 × 3

ㅤㅤ➪ 47

•°• 15ᵗʰ term of the series = 47

Now ,

☯︎ 16ᵗʰ term of the series :

ㅤㅤ➪ a + 15d

ㅤㅤ➪ 5 + 15 × 3

ㅤㅤ➪ 50

•°• 16ᵗʰ term is the series = 50

Now ,

☯︎ 17ᵗʰ term is the series :

ㅤㅤ➪ a + 16d

ㅤㅤ➪ 5 + 16 × 3

ㅤㅤ➪ 53

•°• 17ᵗʰ term of the series = 53

Now ,

☯︎ 18ᵗʰ term of the series :

ㅤㅤ➪ a + 17d

ㅤㅤ➪ 5 + 17 × 3

ㅤㅤ➪ 56

•°• 18ᵗʰ term of the series = 56

And ,

☯︎ 19ᵗʰ term of the series :

ㅤㅤ➪ a + 18 d

ㅤㅤ➪ 5 + 18 × 3

ㅤㅤ➪ 59

•°• 19ᵗʰ term of the series = 59

•°• The complete series is »

➪ 5 , 8 , 11 , 14 , 17 , 20 , 23 , 26 , 29 , 32 , 35 , 38 , 41 , 44 , 47 , 50 , 53 , 56 , 59 , 62

ㅤㅤㅤ꧁ ʙʀᴀɪɴʟʏ×ᴋɪᴋɪ ꧂

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ © BRAINLYxKIKI

Answer 2

In the Given AP

a = 5 ( the first term)

d = 3 ( common difference)

To Find nth term we got a special formula;

$\red{\sf \: n_{th} = a + (n - 1)d}$

In this question we have to answer the 20th term...

So, n = 20;

$\sf \: 20_{th} = 5 + (20 - 1) \times 3 \\ \\ \sf 20_{th} = 5 + 19 \times 3 \\ \\ \sf 20_{th} = 5 + 57 \\ \\ = \sf \: 62$

Hence the 20th term is 62.

I HOPE IT HELPS.