Question

If 18th term of an A.P is 372 and 372 th term of the A.P is 18 ,then which term of this A.P is equal to zero?

Answer 1

If T18th = 372 = a+(18-1)d
and T372th = 18 = a+(372-1)d

therefore, equations will be

a + 17d = 372------------------------------(1)
a + 371d = 18-------------------------------(2)

Now, In equation 1
a = 372 - 17d ------------------------(R1)

Now Putting R1 in equation 2

372 - 17d + 371d =18
372-18 = -371d +17d
354 = -354d
d = -1 ----------------------------(R2)

Now, Putting R2 in equation 1

a + 17d =372
a + 17(-1) = 372
a - 17 = 372
a = 372 + 17
a = 389 -------------------------(R3)

Now, as we have to find term in A.P. which equals to zero,

T = a + (n-1)d
By Putting all the values that is of "a" and "d"

0 = 379 + (n-1)(-1)
0 = 379 - n +1
0 = 380 - n
therefore, n = 380

Answer:- 380th term will be zero

Answer 2

Answer:

380th term will be zero

Step-by-step explanation: