the first term of ap is 5 and the last term is 45 and yhe sum is 400 find the number of terms and the comman difference
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In an AP,
First term (a) = 5
Last term (l) = 45
Sum of the terms of the AP (Sn) = 400
Number of terms = (n) = ?
Common difference = (d) = ?
Now,
Sn = n/2 × (a + l)
=> 400 = n/2 × (5 + 45)
=> n/2 × 50 = 400
=> n = (400 × 2)/50
=> n = 16
Again,
l = a + (n - 1)d
=> 45 = 5 + (16 - 1) × d
=> 45 - 5 = 15d
=> d = 40/15 = 8/3
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