Question

find the sum of first 50 terms of A.P=5,10,15,20​

Answer 1

To find:-

• Sum of 50 terms.⠀⠀⠀

Solution:-

We know that,

Sum of n terms of A.P =$\frac{n}{2}[2a \: + \: (n - 1)d]$

In which,

• n = Number of terms.
• a = First term of A.P.
• d = Common difference.

⠀⠀⠀

➣n = Number of terms = 50 terms.

➣a = First term = 5

➣d = a₂ - a₁ (a₁ = 5 and a₂ = 10)

= 10 - 5

= 5

Common difference = 5.

⠀⠀⠀

So, Put the a , n and d in formula,

$\implies \sf \: \frac{50}{2} [2 \times 5 + (50 - 1) \times 5]$

$\implies \sf \frac{50}{2}[10 + (49) \times 5]$

$\implies \sf \: \frac{50}{2}[10 + 245]$

$\implies \sf \: \frac{50}{2}\times255$

$\implies \sf \: \frac{12750}{2}$

$\implies \sf \: 6375$

Therefore,

❛Sum of 50 terms of A.P is 6375.❜

Answer 2

Answer:

Here a=5

d=a2-a1=10-5=5

n=50

using Sn formula

Sn=n/2[2a+(n-1)d]

S50=50/2[2*5+(50-1)*5]

S50= 25[10+49*5]

S50=25[10+245]

S50=25[255]

S50=6375