Question

The first term of an AP is 5, the last term is 50 and the sum is 440. Find the number of terms and the common difference

Answer 1

$\red{\huge{\underline{Answer}}}$

$\boxed{\huge{Common \: difference =3}}$

Given:

First term, a = 5

Last time, l = 50

Sum, Sn = 440

Number of terms, n = ?

To find:

Common difference = d

Using the below formula to find the value of 'n'

$\boxed{\huge{ S_{n} = \dfrac{n}{2} (a + l)}}$

$440 = \frac{n}{2} \times (5 + 50) \\ \\ 440 = \frac{n}{2} \times 55 \\ \\ n = \frac{880}{55} = 16$

Therefore, number of terms is 16.

Now,

To find the Common difference:

$\boxed{\huge{ l = a + (n-1)d}}$

$50 = 5 + (16 - 1)d \\ \\45 = 15d \\ \\ d = \frac{45}{15} = 3$

Therefore, the common difference(d) is 3.

Answer 2

Answer:-

• a = 5
• an = l = 50
• sn = 440

We need to find,

• d = ?
• n = ?

Finding the number of terms:-

The Formula to be used:- Sn = n/2 (a + l)

➜ 440 = n/2 (5 + 50)

➜ 440 = n/2 (55)

➜ 440/55 = n/2

➜ 40/5 = n/2

➜ 8 = n/2

➜ n = 16

Finding the common difference of the arithmetic progression:-

The Formula to be used:- an = a + (n - 1)d

➜ 50 = 5 + (16 - 1)d

➜ 50 = 5 + (15)d

➜ 50 - 5 = (15)d

➜ 45 = (15)d

➜ d = 45/15

➜ d = 9/3

➜ d = 3

$\rule{200}2$