2) In an arithmetic sequence if its 8th term is 21 and 21th term is 8. a) What is its common difference? b) What is its 29th term? c) What is the sum of first 57 terms of this sequence?
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Step-by-step explanation:
given:
t8= 21
t21= 8
Solution:
t8= a + (n-1) d
21 = a + (8-1) d
21= a + 7d ... (i)
t21= a + (n-1) d
8= a + (21-1) d
8= a + 20d. .... (ii)
therefore, subtracting ii from i
a + 7d = 21
a + 20d = 8
(-) (-) = (-)
__________
13d = 13
d = 1
therefore, substituting d in (i),
21= a + 7 (1)
21= a + 7
a= 21-7
a= 14
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