Question

the 4th and 8th term of an AP are 43 and 95 respectively. find the first term and common difference of the AP describe this question solutions​

Answer 1

Answer:

a = 4, d = 1

Step-by-step explanation:

Let the first term of this AP be a and common difference be d.  

  In APs: nth term = a + ( n - 1 )d.

4th term = 43

⇒ a + 3d = 43  ⇒ a = 43 - 3d

8th term = 95

⇒ a + 7d = 95

⇒ 43 - 3d + 7d = 95

⇒ 4d = 95 - 43

⇒ 4d = 52

⇒ d = 52/4 = 13

     Hence, a = 43 - 3d

                     = 43 - 3(13)

                     = 43 - 39

                     = 4

Hence first term of the AP is 4 and common difference is 4.

Answer 2

Answer:

The 4th term of an AP can be written as a+3d.

$43 = a + 3d$

Similarly,

$95 = a + 7d$

So we can say 8th term - 4th term:

$(a + 7d) - (a + 3d) = 95 - 43 \\ (7 - 3)d = 52 \\ 4d = 52 \\ d = \frac{52}{4} \\ d = 13$

$a + (7)(13) = 95 \\ a + 91 = 95 \\ a = 95 - 91 \\ a = 4$

Hope this helps.

Thanks.

Thus,