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The first term of an ap …

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The first term of an ap is 5 and the last term is 45 and the sum is 400. Find the number of terms and common differences.

Posted by Bharath Kori 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

Here, a = 5
l = 45
S = 400
We know that
{tex}S = \frac{n}{2}(a + l){/tex}
{tex} \Rightarrow 400 = \frac{n}{2}(5 + 45){/tex}
{tex} \Rightarrow 400 = \frac{n}{2}(50){/tex}
{tex} \Rightarrow 400 - 25n{/tex}
{tex} \Rightarrow n = \frac{{400}}{{25}}{/tex}
{tex} \Rightarrow n = 16{/tex}
Hence, the number of terms is 16.
Again, we know that
l = a + (n - 1)d
{tex} \Rightarrow {/tex} 45 = 5 + (16 - 1)d
{tex} \Rightarrow {/tex} 45 = 5 + 15d
{tex} \Rightarrow {/tex} 40 = 15 d
{tex} \Rightarrow d = \frac{{40}}{{15}} = \frac{8}{3}{/tex}
Hence, the common difference is {tex}\frac{8}{3}{/tex}.

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