Question

17. The first term of AP is 5, the last term is 45 and the sum of n term is 400.Find the numbers of terms and common diffrence​

Answer 1

Answer:

given

a=5

l=45

Sn= 400

N=?

Sn=n/2 (a+l)

400=n/2(5+45)

400*2/50=n

8*2=n

n=16

Answer 2

Answer:

The first term of AP is 5, the last term is 45 and the sum of n term is 400.Find the numbers of terms and common difference.

First term of AP = a = 5

Last term of AP = l = 45

The sum of n terms = 400

We have a formula for sum of terms , S = $\frac{n}{2}(a + l)$

So S = $\frac{n}{2}*(5 + 45)$

    400 = $\frac{n}{2}$ * (50)

     $\frac{400}{25}$  = n

    => n = $\frac{80}{5}$

   => n = 16

The numbers of terms = 16 terms

We know first term = a = 5

Last term = a_16 = a + (15 d) = 45

                              => 5 + 15 d = 45

                              =>       15 d =40

                              =>              d = 40/15

So common difference , d = 8/3