Question

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

Answer 1

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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