Question

first term of ap is 5 and last term is 45 and the sum is 400 then dind number of terms and common difference​

Answer 1

Hey mate.

Here's your answer in the given attachment.

Answer 2

Step-by-step explanation:

$\bf\large\underline\purple{Given:-}$

$\displaystyle \sf \bigstar \: \: a1 = 5 \: \: \: \: \: \: \\ \\ \displaystyle \sf \bigstar a(n) = 45 \: \: \\ \\ \displaystyle \sf \bigstar s(n) = 400$

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$\bf\large\underline\purple{Formulas:-}$

$\displaystyle \sf \bigstar \: \: \: \boxed{ \underline{ \boxed{ \bold{a(n) = a + (n - 1)d}}}} \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \bigstar \: \: \: \boxed{ \underline{ \boxed{ \bold{s(n) = \frac{n}{2} (2a + (n - 1)d)}}}}$

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$\bf\large\underline\purple{Solution:-}$

$\displaystyle \sf \bigstar \: \: \: {\bold{a(n) = a + (n - 1)d}} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow \: 45 = 5 + (n - 1)d \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow \: 40 = (n - 1)d \: \: \: \: \: \: \small{ \rm{ \green{equation \: 1}}} \\ \\ \\ \displaystyle \sf \bigstar \: \: \: {\bold{s(n) = \frac{n}{2} (2a + (n - 1)d)}} \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow \: = 400 = \frac{n}{2} \times 50 \: \: \small{ \rm{ \green{for \: equation \: 1}}} \\ \\ \displaystyle \sf \longrightarrow \small{ \rm {\green{n \: = 16}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$