Question

The sum of second and 19th elements in a arithmetic progression is equal to the sum of 8th

Answer 1

Hello Students,

# Complete question -

Q. The sum of 2nd and 19th term of a.p. is equal to the sum of 8th, 15th and 12th term . find the term which is 0 ?

◆ Answer -

14th term will be 0.

◆ Explanation -

Consider an AP with first term a and common difference d.

Given that,

t2 + t19 = t8 + t12 + t15

(a+d) + (a+18d) = (a+7d) + (a+11d) + (a+14d)

2a + 19d = 3a + 32d

a = -13d

Let nth term of AP have value zero.

tn = 0

a + (n-1)d = 0

-13d + (n-1)d = 0

n-1 = 13

n = 14

Therefore, 14th term of AP will be zero.

Hope this helps you.

Answer 2

Answer:

Step-by-step explanation:

The simplest way to crack these kind of questions is :

As Sum of 2nd and 19th term is equal to sum of 8th 15th 12th terms of progression then :

(8 + 15 + 12) - (2 + 19) = 14

So 14th term of progression will be zero.

Similarly you can verify with following question :

Que. The sum of 3rd and 15th elements of an arithmetic progression is equal to the sum of 6th, 11th and 13th elements of the same progression. Then which element of the series should necessarily be equal to zero?

Ans. 12th term will be 0.