Question

The first term of an AP is 5, the last term is 45 and the sum is 400. find the number of films and the common difference

Answer 1

Answer:

Given :

First term = a = 5

Last term = l = 45

Sum of all the terms = S = 400

We know that, l = a+(n-1) d

Using the same formula,

⇒ 45 = 5+(n-1) d

⇒ (n-1) d = 40 -----(1)

Now, S = n/2 (2a+(n-1)d)

Using the given formula,

⇒ 400 = n/2 (2a+40)

(Using equation 1)

⇒ 400 = n/2 [2(a+20)]

(Taking 2 as common)

⇒ 400 = n(5+20)

(Using a = 5)

⇒ 400 = 25n

⇒ n = 400/25

⇒ n = 16 ------(2)

From equation 1 and 2,

⇒ (n-1) d = 40

⇒ (16-1) d = 40

⇒ 15d = 40

⇒ d = 40/15

⇒ d = 2.666

Hence,

Number of terms = n = 16

Common difference = d = 2.66

Answer 2

Given :-

The first term of an AP is 5, the last term is 45 and the sum is 400.

To Find :-

Number of terms

Common difference

Solution :-

We know that

aₙ = a + (n - 1) d

45 = 5 + (n - 1)d

45 - 5 = (n - 1)d

40 = (n - 1)d

Now

Sₙ = n/2 {2a + (n - 1)d}

400 = n/2 {2a + 40}

400 × 2 = n {2a + 40}

800 = n × 2(a + 20)

800/2 = n(a + 20)

400 = n(5 + 20)

400 = 25n

400/25 = n

16 = n

Finding common difference

(16 - 1)d = 40

15d = 40

d = 40/15

d = 8/3

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