In an arithmetic sequence U1 =1.3 , U2= 1.4 and Uk = 31.2 a) find the value Of k b) find the exact value of Sk c) Consider the terms, of this sequence such that n ≤k. Let F be the sum of the terms for which is not a multiple of 3. Show that F= 3240
Answers
Given : an arithmetic sequence U1 =1.3 , U2= 1.4 and Uk = 31.2
To Find : value of k
Solution:
U1 =1.3
U2= 1.4
Uk = 31.2
a = 1.3
d = 1.4 - 1.3 = 0.1
Uk = 1.3 + (k - 1)(0.1)
=> 1.3 + (k - 1)(0.1) = 31.2
=> (k - 1)(0.1) = 29.9
=> k - 1 = 299
=> k = 300
Sk = (300/2)(1.3 + 31.2)
= 150 * (32.5)
= 4875
F be the sum of the terms for which term is not a multiple of 3
3rd term = 1.5
6th term = 1.8
300th term = 31.2
Total terms = 100
Sum = (100/2)(1.5 + 31.2) = 1635
F = 4875 - 1635 = 3240
QED
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