Question

the first term of A. P. is -4 and 10th term is 14. I determine the 30th term

Answer 1

a = -4
a+9d=14
-4+9d=14
9d=18
d=2

30th term=a +29d
=-4+58=54


hey , hope this helps u dear friend

Answer 2

Given:

We have first term is -4 and  10th term is 14.

To Find:

We have to determine the 30th term of A.P?

Step-by-step explanation:

• A.P we will say the terms are in A.P when the difference between the terms is same.
• We have given first term of A.P is -4.
• 10th term of A.P is 14.

• We know nth term of the A.P is given by the formula

       $a_n=a+(n-1)d$

• We have n=10 put in above equation we get

        $a_1_0=a+9d$

• Now, we have first term of A.P is a=-4

       $14=-4+9d$

• Now simplify the above equation we will get

        $14+4=9d\\18=9d\\d=\frac{18}{9}=2$

• Now 30 th term of the A.P is given by the formula

• $a_3_0=a+29d\\a_3_0=-4+29(2)$
  Simplify the above equation as the rule of bodmas

      $a_3_0=54$

Hence, 30th term of the A.P is 54.