please answer fast
Consider the arithmetic sequence 1,8,15,22.......
a) what is the common difference?
b) What will be the remainder when the terms are
divided by its common
difference ?
c) which is the first there digit term of this sequence?
d) with write the algebraic form of this sequence
e) How many terms are there below 100 in this sequence?
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Answer:
a) 7
b) the remainder will be the previous term
c) 16th term
d) tₙ = 7n-6
e) 15 terms
Step-by-step explanation:
a) 8-1 = 7
b) the remainder will be the previous term
c)
a=1, d = 7,
tₙ >99
a+(n-1)d >99
1 + (n-1)7>99
1+7n-7 > 99
7n > 99+6
7n > 105
n > 105/7
n > 15
16th term is the first 3 digit term
d) tₙ = a + (n-1)d
tₙ = 1+(n-1)(7)
tₙ = 1+7n-7
tₙ = 7n-6
6) from question c, it is obvious that there are 15 terms below 100
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