Question

The sum of the first 9 terms of an arithmetic sequence is 270.what s the 5 th term of this sequence ?
write the arithmetic sequence? and common difference


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Answer 1

Answer:

Since you know the last term and the sum you can write an equation where the unknown will be the common difference d. The last (tenth) term is 80 which is greater by d than the ninth term. The ninth term is therefore 80-d, similarly the eigth term is 80–2d etc.

It looks like this: 80+(80-d)+(80–2d)+(80–3d)+(80–4d)+(80–5d)+(80–6d)+(80–7d)+(80–8d)+(80–9d)=530

Now we just sum up all 80s and the unknowns:

800–45d=530 and solve for d

-45d=-270

d=6 So the common difference is 6.

We know from above that the first term is 80–9d so we just plug in d=6.

The first term is 80–9*6=26.

hope it helps you