Question

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.

#Exam - time.


#No - Spams!

Answer 1

$\huge{\boxed{\tt{Answer:-}}}$

Given:-

a = 5

l = 45

Sn = 400

$\huge{\boxed{\tt{Explanation:-}}}$

Sn = n/2 (5+45)

400 × 2 = n × 50

800/50 = n

$\large{\boxed{\tt{16 = n}}}$

Therefore:-

Number of terms is 16

an = 5 + (16-1)d

400 - 5 = (16-1)d

395 = (15) d

395/15=d

395/15=d

79/3 = d

$\large{\boxed{\tt{d = 26.33}}}$

Answer 2

Answer:

n=16 and d = 8/3

Explanation:

a=5

l=45

s=400

s=(n÷2)(a+l)

so 400 =(n÷2)(5+45)

400=(n÷2)50

(n÷2) =(400÷50) =8

n =8×2 =16

so number of terms = 16

now

l = a+(n-1)d

so 45= 5+(16-1)×d

45 -5 =15d

15d = 40

d =40 ÷15

d= 8/3