Question

the first term of an arithmetic progression is 1 and the sum of the first 15 term is 225 find the common difference

Answer 1

Answer:

s15=975

Explanation:

Consider the following example:

The first term of an arithmetic sequence is 2 and the third is 6. What is d, the common difference?

With an arithmetic sequence, the d is added to each term to get the next.

Since t1=2 and t3=6, there will be 3−1=2d's added to t1 to get t3. So, we can write the following equation:

2+2d=6

2d=4

d=2

It works, too, since if t1=2, t2=4 and t3=6, which makes an arithmetic sequence.

The same principle can be applied to our problem.

25−1=24, so there will be 24d's added to 51to get 99. 

Hence, 51+24d=99

24d=48

d=2

So, the common difference is 2.

All we have to do now is to apply the formula sn=n2(2a+(n−1)d)) to determine the sum of the sequence.

s15=152(2(51)+(15−1)2)

s15=152(102+28)

s15=152(130)

s15=975

Thus, the sum of the first fifteen terms in the arithmetic sequence is 975.

Hopefully this helps!

Answer 2

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