Question

The first term of an A.P is 5 and last term is 45 and the sum is 400. Find the number of term and the common difference.

Answer 1

Answer:

In an AP,

First term (a) = 5

Last term (l) = 45

Sum of the terms of the AP (Sn) = 400

Number of terms = (n) = ?

Common difference = (d) = ?

Now,

Sn = n/2 × (a + l)

=> 400 = n/2 × (5 + 45)

=> n/2 × 50 = 400

=> n = (400 × 2)/50

=> n = 16

Again,

l = a + (n - 1)d

=> 45 = 5 + (16 - 1) × d

=> 45 - 5 = 15d

=> d = 40/15 = 8/3

✨Hope it will help you.✨

Answer 2

Answer:GIVEN:

first term(a)=5

last term(l)=45

sum of AP(Sn)=400

TO FIND:

no. of terms(n) ,and common difference(d)

NOW,

we know,

Sn=n/2(a+l)

400=n/2(5+45)

800=n(50)

n=800/50

so,n=16

we know,

l=a+(n-1)d

l=5+(n-1)d

45=5+ (16-1)d

45=5+15d

45-5=15d

40/15 =d

so,d=8/3

no. of terms =16

Common difference=8/3 or 2.66I

HOPE IT WILL HELP YOU...