28. 23' term of an arithmetic sequence is 32 and its 35'h term is 104.
a) What is its common difference?
b) What is its first term?
c) Is the difference of any two terms of this sequence be 90?
d) Find the sum of the first 35 terms?
Answers
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★ solution →
a) what is its common difference?
we know that,
then,
and,
now we have two equations,
32 = a + 22d ......(i)
104 = a + 34d ......(ii)
now, subtract eq.(i) from eq.(ii)
so,common difference of the AP is 6
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b) what is its first term?
from first part we get.
common difference(d) = 6
now, put the value of d in eq.(i)
so, first term of AP is -100
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c) is the difference of any two terms of this sequence be 90?
we know that,
common difference of this AP is 6
so, difference of nth term and (n+15)th term is 90
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✩ for verification ✩
☞ let n = 1 , then n+15 = 16
from 2nd part we have,
now we have to find 16th of this AP
now, see difference between these two terms
hence, varified!
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so, we can say yes, here difference of nth term and (n+15)th term of this AP is 90
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d) find the sum of the first 35 terms?
we know that,
and here,
・a = -100
・d = 6
・n = 35
so, sum of first 35 terms of AP is 70
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hence,
- a) common difference = 6
- b) first term = -100
- c) yes, difference of nth term and (n+15)th term of this AP is 90
- d) sum of first 35 terms is 70