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## In another case, p and 2p are the first and second term respectively of an arithmetic progression. The nth term is 336 and the of the first

Question

In another case, p and 2p are the first and second term respectively of an arithmetic progression. The nth term is 336 and the of the first n terms is 7224. Write down two equations in n and p and hence find the values of n and p

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Mathematics
3 years
2021-07-20T05:18:08+00:00
2021-07-20T05:18:08+00:00 1 Answers
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## Answers ( )

Consecutive terms in this sequence differ by

p.First term:

pSecond term:

p+p= 2pThird term: 2

p+p= 3pand so on. It follows that the

n-th term satisfiesnp= 336Presumably you meant to say the “sum of the first

nterms” is 7224, which is to sayp+ 2p+ 3p+ … +np= 7224which can be rewritten as

p(1 + 2 + 3 + … +n) = 7224p(n(n+ 1)/2) = 7224n(n+ 1)p= 14,448Substitute the first equation in the second one and solve for

n:336 (

n+ 1) = 14,448n+ 1 = 43n= 42Now solve for

p:42

p= 336p= 8