Question

the first term of sn Ap is 5 the last term is 45 and the sum is 500 .find the number of terms and the common difference .

Answer 1

solution :-

let n be the number of term an Ap and d is the common difference.

given term in the questions .

first term a = 5

last term = 45

and sum of n terms = 500

$Sn = \frac{n}{2} (a \: + l) \\ \\ 500 \: = \frac{n}{2} (5 + 45) \\ \\ 500 \times 2 = 50n \\ \\ n \: = \frac{500 \times 2}{50} \\ \\ = 10 \times 2 = 20 \\ \\ l = 45$
using formula

[ l = a ( n -1) d ]

=> a + ( n -1) d = 45

here ,

first term ( a) = 5

number of terms ( n) = 20


=> 5 + ( 20 -1) d = 45

=> 19d = 45 - 5 = 40

$d = \frac{40}{19}$

therefore the number of terms is 16 and the common difference is $\frac{40}{19.}$



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Answer 2

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