Question

the frist term ogf an ap is 5,the last term is45and the sum is 400.find number of term and the common difference .​

Answer 1

GIVEN :

First of an AP = a = 5

Last term of an AP = an = 45

Sum of the AP = 400

We know that,

In an AP, sum of terms = n/2 [ a + an ]

400 = n/2 [ 5 + 45 ]

400 = n/2 [ 50 ]

400 × 2 = 50n

800 = 50n

n = 800/50

n = 16

Number of terms = 16

Now,

Substitute n in an formula to find [d]

We know that,

In an AP, nth term = a + (n - 1)d

45 = 5 + (16 - 1)d

45 = 5 + (15)d

45 = 5 + 15d

15d = 45 - 5

15d = 40

d = 40/14

d = 8/3

Common Difference = 8/3

Therefore, n is 16 and difference is 8/3.

Answer 2

Answer:

Step-by-step explanation:

Given :-

First term (a) = 5

Last term (l) = 45

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

To Find :-

Number of terms = (n) = ?

Common difference = (d) = ?

Formula to be used :-

Sn = n/2 × (a + l) and l = a + (n - 1)d

Solution :-

Number of terms (n)

⇒ Sn = n/2 × (a + l)

⇒ 400 = n/2 × (5 + 45)

⇒ n/2 × 50 = 400

⇒ n = (400 × 2)/50

⇒ n = 16

Common difference (d)

⇒ l = a + (n - 1)d

⇒ 45 = 5 + (16 - 1) × d

⇒ 45 - 5 = 15d

⇒ d = 40/15 = 8/3

Hence, number of terms in AP is 16 and common difference is 8/3 .