Question

12th term of the Ap 5,8√_11,14​

Answer 1

Answer:

12th term of the Ap 5,8√_11,14 is 38

Step-by-step explanation:

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Answer 2

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Given:

AP sequence = 5,8,11,14

To find:

12th term of AP = ?

Solution:

$\\ \\ tn \: = a + (n - 1)d \\ \\ where \: \: \: \: a \: = first \: term \\ \\ n = term \: to \: find \\ \\ d = common \: difference \: \\ between \: terms$

Solving for common difference (d)

8 - 5 = 3

14 - 11 = 3

Here, common difference (d) is 3

n = 12

a = 5

$\\ \\ t12 = 5 + (12 - 1)3 \\ \\ = 5 + 11 \times 3 \\ \\ = 5 + 33 \\ \\ = 38 \\ \\ t12 = 38$

Required answer:

Thus 12th term of Arithmetic progression 5,8,11,14 is 38

Cross check:

Let's find n= ? if tn = 38, d = 3, a = 5

$\\ \\ tn = a + (n - 1)d \\ \\ 38 = 5 + (n - 1)3 \\ \\ 38 = 5 + 3n - 3 \\ \\ 38 - 5 = 3n - 3 \\ \\ 33 = 3n - 3$

$\\ \\ 33 = 3n - 3 \\ \\ 33 + 3= 3n \\ \\ 36= 3n \\ \\ \dfrac{36}{3} = n \\ \\ 12 = n$

Hence, proved our calculation is correct

Basic points:

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