Question

The first and the last term of an ap 5 and 45 respectively if the sum of all is term is 400 then find its common difference

Answer 1

Arithmetic Progression

→ an = a + (n - 1)d

• a = first term
• an = Required term
• n = number/placing term
• d = common difference

→ 45 = 5 + (n - 1)d

→ 40 = (n - 1)d

→ 400 = n/2 × [2(5) + (n - 1)d]

→ 800 = n[10 + 40]

→ 800/50 = n

→ 16 = n

Hence, 40 = (16 - 1)d

→ 40 = 15d

→ 8/3 = d

Hence common difference os 8/3.

Answer 2

$\bold {\huge {Your ~answer :-}}$

$\bf\huge\boxed{8/3}$

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Given

a1 = 5

l = 45

Sn = 400

Explanation —

We know

Sn = n/2 (a+l)

400 = n/2(5+45)

n/2 = 8

n = 16

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Now

as we know last term and first term

So we can apply AP formula

45= 5 +(16-1)d

d = 40/15

d = 8/3

therefore the common difference is 8/3