Question

the sum of 2nd and 19th term of A.P. is equal to the sum of 8th , 15th and 12 th term . find the term which is 0; the sum of 2nd and 19th term of A.P. is equal to the sum of 8th , 15th and 12 th term . find the term which is 0

Answer 1

hence , 13th term of AP .

Answer 2

Answer:

The 14th term is 0.

Step-by-step explanation:

Formula of nth term in AP = $a_n=a+(n-1)d$

where a = first term , d = common difference , n is the term no.

Now we are given that the sum of 2nd and 19th term of A.P. is equal to the sum of 8th , 15th and 12th term .

$\Rightarrow a_2+a_{19}=a_8+a_{15}+a_{12}$

Using formula

$\Rightarrow a+(2-1)d+a+(19-1)d=a+(8-1)d+a+(15-1)d+a+(12-1)d$

$\Rightarrow a+d+a+18d=a+7d+a+14d+a+11d$

$\Rightarrow 2a+19d=3a+32d$

$\Rightarrow a=-13d$

Now we are supposed to find which term is 0

So, $0=a+(n-1)d$

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

$13d=(n-1)d$

$13=(n-1)$

$14=n$

Hence The 14th term is 0.