Question

the 11th term and the 21st term of an ap are 16 and 29 respectively find the 41st term of this AP​

Answer 1

Step-by-step explanation:

answer is explained in detail in the above picture

Answer 2

$\sf{\huge{\underline{\orange{Given :-}}}}$

• The 11th term and the 21st term of an ap are 16 and 29 respectively .

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The 41st term of this AP.

$\sf{\huge{\underline{Answer :-}}}$

Let the first term be a & the common difference be d.

We have, The 11th term and the 21st term of an ap are 16 and 29 respectively .

We know ,

Nth term = a + ( n - 1 ) d

Case 1 :-

The 11th term is a + ( 11 - 1 ) d

➝ 16 = a + 10d _____{1}

Case 2 :-

The 21st term is a + ( 21 - 1 ) d

➝ 29 = a + 20d _____{2}

From ( 1 ) and ( 2 ), we get ,

a + 10d = 16 _____{1}

a + 20d = 29 _____{2}

- - -

___________________

- 10 d = -29 + 16

___________________

➝ 29 - 20d = 16 - 10d

➝29 - 16 = 20d - 10d

➝13 = 10d

➝ d = 13 / 10

➝ d = 1.3 _____{3}

Putting 3 in 1,

a + 10 × 1.3 = 16 _____{1}

➝ a + 13 = 16 _____{1}

➝ a = 16 - 13

➝ a = 3

Nth term = a + ( n - 1 ) d

The 41st term of this AP = 3 + ( 41 - 1 ) 1.3

➝ 3 + ( 40 ) 1.3

➝ 3 + 52

➝ 55.

Hence , 41st term of this A.P. is 55.