Question

Which term of an ap is 17,if 3rd term is 38 and 8th term of the ap is 23

Answer 1

a3 a+2d=38

a8 a+7d=23
which gives d= -3
substitute in a+2d=38
a+2×-3=38
a=44
a17= a+16d
44+16×-3=_4

Answer 2

Answer:  17 is the 10th term of the A.P.

Step-by-step explanation:  Given that the 3rd term of an A.P. is 38 and 8th term is 23.

We are to find the number of the term with value 17.

We know that

if a and r represents the first term and the common difference of an A.P., then its nth term is given by

$a_n=a+(n-1)d.$

According to the given information, we have

$a_{3}=38\\\\\Rightarrow a+(3-1)d=38\\\\\Rightarrow a+2d=38~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and

$a_{8}=23\\\\\Rightarrow a+(8-1)d=38\\\\\Rightarrow a+7d=23~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Subtracting equation (i) from equation (ii), we get

$7d-2d=23-38\\\\\Rightarrow 5d=-15\\\\\Rightarrow d=-\dfrac{15}{5}\\\\\Rightarrow d=-3.$

From equation (i), we get

$a+2\times(-3)=38\\\\\Rightarrow a=38+6\\\\\Rightarrow a=44.$

Therefore, if nth term is 17, then we get

$a_n=17\\\\\Rightarrow 44+(n-1)(-3)=17\\\\\Rightarrow 44-3n+3=17\\\\\Rightarrow 3n=47-17\\\\\Rightarrow 3n=30\\\\\Rightarrow n=10.$

Thus, 17 is the 10th term of the A.P.