Question

If the first term of an AP is 10 and the last term is 450 and the sum is 180 then find the common difference

Answer 1

Given :

First term (a) =10

Last term (l) =450

Sum of the terms (Sn) =180

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To FiND :

The common difference (d) =?

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Formula UseD:

$Tn \: =a+(n-1)d$

$Sn \: = \frac{n}{2} (2a + (n - 1)d)$

$Sn \: = \frac{n}{2} (l + a)$

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SolutioN:

$Sn \: = \frac{n}{2} (l + a)$

$180 = \frac{n}{2} (450 + 10) \\ 180 = \frac{n}{2} (460) \\ 180 = 230n \\ n = \frac{18}{23}$

$l \: = a + (n - 1)d \\ 450 = 10 + ( \frac{18}{23} - 1)d \\ 450 - 10 = - \frac{5}{23} d \\ 440 = - \frac{5}{23} d \\ d \: = - \frac{440 \times 23}{5} \\ d \: = - 2024$

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Therefore, the common difference is - 2024.

Answer 2

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$\huge\tt{GIVEN:}$

• The first term of an AP is 10 and the last term is 450

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$\huge\tt{TO~FIND:}$

• The common difference

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$\huge\tt{SOLUTION:}$

➠Sum of the terms = ⁿ/2(l+b)

➠180= ⁿ/2(450+10)

➠180 = 230n

➠18/23 = n

➠l = a + (n-1)d

➠450 = 10 + (18/23-1)d

➠450 - 10 = - 5/23d

➠440 = 5/23

➠440 × 23/5 = d

➠-2024 = D

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