In-an-A-P-the-sum-of-the-first-50-terms-is-6275-Write-this-A-P-knowing-that-the-ratio-is-5-

Question Number 55628 by Mikael_Marshall last updated on 28/Feb/19

I n a n A . P, t h e s u m o f t h e f i r s t 50 t e r m s i s 6275 . W r i t e t h i s A . P . k n o w i n g t h a t t h e r a t i o i s 5 .

Answered by kaivan.ahmadi last updated on 28/Feb/19

s_{n} = \frac{n}{2} [2 a + (n - 1) d]

6275 = 25 [2 a + 49 \times 5] = 25 [2 a + 245] =

50 a + 6145 \Rightarrow 50 a = 6275 - 6145 = 150 \Rightarrow

a = 3

t h e s e q u e n c e i s

3, 8, 13, 18, 23, \dots

a_{n} = a + (n - 1) d = 3 + (n - 1) 5 \Rightarrow

a_{n} = 5 n - 2

Answered by Mikael_Marshall last updated on 28/Feb/19

t h a n k y o u S i r .