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Question:
Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
30
∑ (−3i+5)
i=1
Answer:
The first three terms are : 2, -1 and -4
The last term is: -85
The sum of the sequence is: -1245
Step-by-step explanation:
Given;
==================================
30
∑ (−3i+5) -------------------(i)
i=1
==================================
Where the ith term aₙ is given by;
=
-------------------(ii)
(a) Therefore, to get the first three terms (), we substitute i=1,2 and 3 into equation (ii) as follows;
=
= 2
Since the sum expression in equation (i) goes from i=1 to 30, then the last term of the sequence is when i = 30. This is given by;
(b) The sum of an arithmetic sequence is given by;
-----------------(iii)
Where;
n = number of terms in the sequence = 30
= first term = 2
= last term = -85
Substitute the corresponding values of n, and
into equation (iii) as follows;
= 15[-83]
= -1245