Question

answer the following question
lf the 3rd term and the 9th term of an ap are 4 and -8 respectively, which term of this AP is zero​

Answer 1

Step-by-step explanation:

Hence, 5th term of this A.P. is 0.

Answer 2

Answer:

Hint: The nth term of an arithmetic progression is given as where ‘a’ and ‘d’ are the first time and common difference of the A.P. and is denoting the nth term. Form the equations using the given conditions and solve it further to get the answer.

Complete step-by-step answer:

As we know that general term of an A.P. is given as where a, d are denoting the first term of the A.P. and common difference respectively and is denoting the nth term.

So, now coming to the question, we have the 3rd and 9th terms of the A.P. as 4 and -8 respectively.

Hence, we can form two equations with the help of the relation of the nth term of any A.P.

Let common difference and first term be d and a respectively of A.P. , hence

………….. (i)

So, 3rd term can be written as

As we know , hence, we get

……….. (ii)

Similarly, 9th term can be written with the help of equation (i) as

As we know , hence, we get

a + 8d = -8 ………... (iii)

Now, subtract equation (ii) and (iii) to get values of a and d. hence, we get

(a + 2d) – (a + 8d) = 4 – (-8)

a + 2d – a – 8d = 4 + 8

a – a + 2d – 8d = 12

-6d = 12

d = -2 ……………. (iv)

Now, put the value of ‘d’ from equation (iv) in equation (iii) to get the value of ‘a’. Hence, we get

a + 8 (-2) = -8

a – 16 = -8

a = 16 – 8 = 8

a = 8 ………….. (v)

Hence, the given A.P. in the question will have first term as 8 and common difference as ‘-2’.

Now, we need to determine which term will be zero of the A.P.

Let term of the given A.P. will be O.

Hence, we can write the term from the equation (i) as

Where a = 8 from equation (v), d = -2 from equation (iv) and

So, we get

0 = 8 + (t – 1) (-2)

-8 = (t -1) (-2)

(t -1) = 4

t = 5

Hence, the 5th term of the A.P. will be 0.

Step-by-step explanation:

Hope this help