Question

is the first term of an ap is 5 the last term is 45 and the sum is 400 find the number of terms & common difference???

Answer 1

Hey!!!

Good Afternoon

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For an AP,we have

a = 5
l = 45
Sn = 400
n = ?
d = ?

Thus we know

Sn ⤵️
$= \frac{n}{2} (a + l)$

$= > 400 = \frac{n}{2} (5 + 45)$

=> n(50) = 800

=> n = 16 (Answer)

Now we know l = a + (n - 1)d

=> 45 = 5 + (16 - 1)d

=> 15d = 40

=> d = 8/3 (Answer)

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Hope this helps ✌️

Have a Super Saturday

Answer 2

a=5
a+(n-1)d=45
Sn = n/2*a+l
400=n/2*5+45
400=25*n
n=16
number of terms=16 
a+(16-1)*d=45
5+15d=45
15d=40
d=40/15=8/3 is the common difference.