The first term of an arithmetic sequence is 10 and its common difference is 3
Write the first three terms of the sequence
Verify whether 100 is a term of this sequence?
a) Write its 10th term
b) Write its nth term ( Algebraic form)
c) Can the difference between any two terms of this sequence be 45?
d) Which term of this sequence is 181?
Answers
Step-by-step explanation:
1)The 1st 3 terms in an arthematic sequence are a,a+d,a+2d where a is 1st term and d is common difference.so the three terms are 10,10+3,10+2*3= 10,13,16.
2) nth term of arthematic sequence is a+(n-1)d
so let a+(n-1)d=100
10+(n-1)3=100
3n-3=90
3n=93
n=31
so we can say that 100 is the term of arthematic sequence.
3)nth term of arthematic sequence is a+(n-1)d
so nth term of this sequence is 10+3(n-1)
=10+3n-3
=7+3n
4)Yes. Because 45 is a multiple of 3. Like nd is a multiple of d.
5)Let a+(n-1)d=181
10+(n-1)3=181
7+3n=181
3n=174
n=58
So 181 is 58th term of the arthematic sequence.
Given : The first term of an arithmetic sequence is 10 and its common difference is 3
To Find : first three terms of the sequence
whether 100 is a term of this sequence?
Write its 10th term
Write its nth term
Can the difference between any two terms of this sequence be 45
Which term of this sequence is 181
Solution:
a = 10
d = 3
aₙ = a + (n -1)d
=> aₙ = 10 + (n -1)3
=> aₙ = 3n + 7
nth term = 3n + 7
first three terms of the sequence
10 , 13 , 16
3n + 7 = 100
=> 3n = 93
=> n = 31 hence 31st term is 100
3n + 7 = 181
=> 3n = 174
=> n = 58 58th term is 174
Difference between any 2 terms can be 3k
Hence 45 can be difference
10 + 45 = 55
3n + 7 = 55 => n = 16
Difference between 1st and 16th term = 45
Difference between nth and n + 15 th term will always be 45
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