Question

The first term of finite A.P. is 5, the last term is 45 and the sum is 500. Find the number of

terms.​

Answer 1

Answer:

$\huge{\boxed{\rm{\red{answer=20}}}}$

Step-by-step explanation:

Given:-

The first term of finite A.P. is 5, the last term is 45 and the sum is 500.

To find:-

Find the number of terms in the AP

Solution:-

The first term of an AP(a)=5

The last term(l)=45

The sum of the terms(Sn)=500

Applying formula:-

In an AP ,if the first term is 'a'and the last term is 'l' then The sum of n terms is Sn=n/2(a+l)

=>n/2(5+45)=500

=>n/2(50)=500

=>25n=500

=>n=500/25

=>n=20

Answer:-

No. of terms in the given AP is 20

Answer 2

Answer:

sum=n/2{2a+(n-1).b}. [here a is the 1st term]

n is the number of term and b is the common difference.

again ,

45=5+(n-1).b

(n-1).b=45-5=40

500=n/2{2.5+40}

500=n/2.50

50 n=500.2

n=500.2/50=20

so the number of terms is 20