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Marianna [84]
1 year ago
5

P and q are two arithmetic sequences. The first four terms of sequence P are 2,6,10,14. The nth term of sequence Q is 145-3n. Th

e rth term of sequence P has the same values as the rth term of sequence Q. Work out the value of r.
Mathematics
1 answer:
Tomtit [17]1 year ago
5 0

Answer:

r = 21

Step-by-step explanation:

nth of sequence P :

T_{n} = 4n -2

r^{th} term : 4r-2=145-3r\\4r+3r=145+2\\7r=147\\r=21

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Given the sequence 7, 12, 17, 22, ...
abruzzese [7]

Answer:

option D is true.

Step-by-step explanation:

Given the sequence

7, 12, 17, 22, ...

An arithmetic sequence has a constant difference 'd' and is defined by

a_n=a_1+\left(n-1\right)d

Computing the differences of all the adjacent terms

12-7=5,\:\quad \:17-12=5,\:\quad \:22-17=5

The difference between all the adjacent terms is the same

so

d=5

as

a_1=7

Thus, the nth term of the arithmetic sequence will be:

a_n=5\left(n-1\right)+7

a_n=5n+2

Therefore, option D is true.

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