11. The sum of the first 15 terms of an arithmetic
sequence is 675 and the sum of the first 20 terms is 1150.
a. What is the 8th term?
b. What is the 18th term?
c. What is the first term of the sequence? Find the
algebraic expression of the sequence.
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Third term of an arithmetic sequence is 34 and its eighth term is 69.
(a) Find the common difference of this sequence
(b) Write the algebraic form of this sequence
(c) If a new sequence is formed by multiplying each term of the given sequence by 4 and the adding 3 , what is the tenth term of the new sequence so formed?
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Answer
t
3
=34 and t
8
=69
(a) Now, t
n
=a+(n−1)d
⇒t
3
=a+(2−1)d and t
8
=a+(7−1)d
⇒34=a+(2−1)d and 69=a+(7−1)d
⇒34=a+d and 69=a+6d
Thus, 69−34=a+6d−a−d
⇒35=5d⇒d=7
(b) First term, a=t
3
−2d=34−2(7)=34−14=20
General term, t
n
=a+(n−1)d=20+(n−1)7=20+7n−7=7n+13
Thus, t
n
=7n+13 is the algebraic form of this sequence.
(c) t
n
=7n+13
If each term of the sequence is multiplied by 4 and then 3 is added to it, the
general term will be t
n
=[(7n+13)×4]+3=28n+52+3=28n+55
Thus, tenth term, t
10
=28(10)+55=280+55=335