The first term of an arithmetic sequence is 2 and the fourth term is 11. Find the sum of the first 50 terms.

At the 50th term, you get the number 149. I currently cannot think of a simpler and easier way than to manually add up all the numbers that follow the given equation between 2 and 149 (your 1st and 50th terms). When you add up all those numbers, you get your final answer (as you've given me) of 3775.

Hope this helps!

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vijayhalder031 vijayhalder031 · Answer 2 · 2022-06-10T06:23:51+02:00

The correct answer is 3775

What is Arithmetic Progression?

It is a sequence of numbers such that the difference between the consecutive terms is constant.

How to solve the problem?

The problem can be solved by following steps

The first term given is 2 (a=2)
The 4th term given is 11 (a+3d=11)
We need to find the sum of first 50 terms

We need to find the common difference first

Substituting the value of a in a+3d=11

Therefore 2+3d=11

Therefore 3d = 9

Hence d=3

The common difference is 3

Now , for first 50terms

n = 50

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

Sn = 50/2 (2(2)+(50-1)3)

Sn = 25 (4+147)

Sn = 3775

Hence the sum of first 50 terms is 3775

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