Question

The first term of an A.P. is 1, last term is 50
and the sum is 204. Find the common
difference.​

Answer 1

Answer:

Here's your answer

a= 1

last term (l) = 50

Sum is 204

by

$s = \frac{n}{2} (a + l) \\ \\ 204 \times 2 = n(51) \\ \\ 408 = 51n \\ \\ \frac{408}{51} =n \\ \\ 8 = n$

So

$l = a + (n - 1)d \\ \\ 50 = 1 + 7d \\ \\ 50 - 1 = 7d \\ \\ 49 = 7d \\ \\ \frac{49}{7} = d$

$7 = d$

Hope it helps ✌

Answer 2

The common difference is 7.

Step-by-step explanation:

Given : The first term of an A.P. is 1, last term is 50  and the sum is 204.

To find : The common  difference ?

Solution : ​

The sum formula of A.P is given by,

$S_n=\frac{n}{2}[a+l]$

Where, a=1 is the first term

l=50 is the last term

$S_n=204$ is the sum

Substitute the values,

$204=\frac{n}{2}[1+50]$

$408=51n$

$n=\frac{408}{51}$

$n=8$

Using last term formula,

$l=a+(n-1)d$

$50=1+(8-1)d$

$50-1=7d$

$49=7d$

$d=\frac{49}{7}$

$d=7$

The common difference is 7.

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