Question

THE FIRST TERM OF A.P.IS 5,THE LAST TERMS IS 45 AND THE SUM OF TERMS IS 400.FIND THE NUMBERS OF TERMS AND THE COMMON DIFFERENCE OF A.P

Answer 1

Heya user !!!

Here's the answer you are looking for

Let sum of n terms be 400.

First term (a) = 5

Last term (l) = 45

$sum \: = \frac{n}{2} (a + l) \\ 400 = \frac{n}{2} (5 + 45) = \frac{n}{2} (50) \\ \frac{n}{2} = \frac{400}{50} \\ n = \frac{400 \times 2}{50} = 16$

So number of terms is 16.

Now, l = a + (n - 1)d

So,
$45 = 5 + (16 - 1)d \\ 45 - 5 = 15d \\ 40 = 15d \\ d = \frac{40}{15} = \frac{8}{3}$

The common difference is 8/3.



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Answer 2

Hey there!

NO. OF TERMS (n) = 16

&

COMMON DIFFERENCE (d) =8/3

Complete answer is decribed in the above Pic. ↑↑

HOPE IT HELPED ^_^
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