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

a=5
l=45
Sn=400
so,
Sn=n/2(5+45)
400×2=n×50
800/50=n
16=n
so number of terms is 16
an=5+(16-1)d
400-5=(16-1)d
395=(15)d
395/15=d

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

a = 5

l(Last term) = 45

S = 400

${\boxed{\sf\:{\dfrac{n}{2}(a+l)=400}}}$

★Cross Multiplication :-

n(5 + 45) = 400 × 2

n(50) = 400 × 2

${\boxed{\sf\:{n=\dfrac{400\times 2}{50}}}}$

= 8 × 2

= 16

l(Last term) = 45

a + (n - 1)d = 45

5 + (16 - 1)d = 45

5 + 15d = 45

15d = 45 - 5

15d = 40

${\boxed{\sf\:{d=\dfrac{40}{15}}}}$

${\boxed{\sf\:{d=\dfrac{8}{3}}}}$

★Therefore

${\boxed{\sf\:{Term\;is\;16\;and\;d=\dfrac{8}{3}}}}$