Question

The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms
and the common difference. ​

Answer 1

Answer:

ok not bad but i cant answer

Step-by-step explanation:

Answer 2

•$\large\mathrm\purple{Given}$→

a (first term)= 5

l (last term)= 45

S (sum of n terms)=400

•$\large\mathrm\purple{To\:\: find}$→

n(number of terms)=?

d(common difference)=?

We know that,

$s = \frac{n}{2} \times (a + l)$

$400 = \frac{n}{2} \times (5 + 45)$

$400 = \frac{n}{2} \times 50$

$400 = 25n$

$n = \frac{400}{25}$

$n = 16$

$\large\tt\pink{So,\:\: n=16}$

Also,

$s = \frac{n}{2} \times {2a(n - 1)d}$

$40 0= \frac{16}{2} \times 2 \times 5 + (16 - 1)d$

$400 = 8 \times (10 + 15)d$

$400 = 80 + 120d$

$320 = 120d$

$d = \frac{320}{120}$

$d = \frac{8}{3}$

$\large\tt\pink{So,\:\: d=8/3}$