Formula given to us:

\(Sn = Sn-1 +1.5; s1 = 2 and

An = An-1 - 1.5; A1 = 18.5\)

For the first sequence

Each subsequent value of \(s\) is greater by \(1.5\) For solving the question we need to calculate the sum of first 13 terms

we have the 1st term as \(2\). There remains \(12\) more terms. We know that there is an increase of \(1.5\) per term hence there is a total increase of \(12 * 1.5 = 18\)

Last term of the sequence = \(2+18 = 20\)

Since the sequence is equally spaced avg = \(\frac{2 +20}{2} = 11\)

There are a total of \(13\) terms hence sum of the sequence = \(11* 13 = 143\)

For the second sequence

Each subsequent value of A is less by \(1.5\) For solving the question we need to calculate the sum of first \(13\) terms

we have the 1st term as \(18.5\) There remains \(12\) more terms. We know that there is a decrease of \(1.5\) per term hence there is a total decrease of \(12 * 1.5 = 18\)

Last term of the sequence = \(18.5 - 18 = 0.5\)

Since the sequence is equally spaced avg = \(\frac{0.5 +18.5}{2} = 9.5\)

There are a total of \(13\) terms hence sum of the sequence = \(9.5* 13 = 123.5\)

Option A

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This is my response to the question and may be incorrect. Feel free to rectify any mistakes