Question

please answer the question please​

Answer 1

Given :-

◉ We are given an AP, In which

10 times 10th term is equal to thirty times of 30th term.

To Find :-

◉ 40th term of the AP

Solution :-

We know,

⇒ aₙ = a + (n - 1)d

Where, n = position of term

So, As given in the Question,

⇒ 10 ( 10th term ) = 30 ( 30th term )

⇒ 10 [ a + (10 - 1)d ] = 30 [ a + (30 - 1)d ]

⇒ 10 ( a + 9d ) = 30 ( a + 29d )

⇒ 10a + 90d = 30a + 870d

⇒ 20a + 780d = 0

Divide both sides by 20

⇒ a + 39d = 0

⇒ a + (40 - 1)d = 0

⇒ 40th term = 0

Hence, 40th term of the given AP is 0.

Some Information :-

☛ An AP is a sequence of numbers in which difference of each consecutive terms are same. Which is also known as Common Difference.

☛ Sum of n terms = n / 2 [ 2a + (n - 1)d ]

Sₙ = n / 2 [ a + aₙ ]