The sum of the first term and the last term of an AP is 51. The second

1.	The sum of the first term and the last term of an AP is 51. The second last term is 42. Find the second term.1. 92. 73. 84. 6
Answer» Correct Answer - Option 1 : 9 Given: The sum of the first term and the last term is 51. The second last term is 42. Formula: Nth term of an AP, T_n= a + (n - 1)d, where ‘a’ is the first term, ‘n’ is the total number of terms and ‘d’ is the common difference. Calculation: Let the first term is ‘a’ and common difference is ‘d’. From the question a + T_n= 51 ⇒ a + a + (n – 1)d = 51 ⇒ 2a + (n – 1)d = 51 -----(1) Second last term = 42 T_{(n- 1 )} = 42 ⇒ a + (n – 2)d = 42 ----(2) Subtracting equation (2) from (1) we get a + (n – 1)d – (n – 2)d = 9 ⇒ a + nd –d –nd + 2d = 9 ⇒ a + d = 9 Second term = a + d = 9 ∴ required answer is 9.

The sum of the first term and the last term of an AP is 51. The second last term is 42. Find the second term.1. 92. 73. 84. 6

Answer» Correct Answer - Option 1 : 9

Given: The sum of the first term and the last term is 51. The second last term is 42.

Formula:

Nth term of an AP, T_n= a + (n - 1)d, where ‘a’ is the first term, ‘n’ is the total number of terms and ‘d’ is the common difference.

Calculation:

Let the first term is ‘a’ and common difference is ‘d’.

From the question

a + T_n= 51

⇒ a + a + (n – 1)d = 51

⇒ 2a + (n – 1)d = 51 -----(1)

Second last term = 42

T_{(n- 1 )} = 42

⇒ a + (n – 2)d = 42 ----(2)

Subtracting equation (2) from (1) we get

a + (n – 1)d – (n – 2)d = 9

⇒ a + nd –d –nd + 2d = 9

⇒ a + d = 9

Second term = a + d = 9

∴ required answer is 9.