OE


According to the information the sequence is Arithmetic Progression. Let us assume that 𝑀1 = 𝑎

𝑀 2 = 𝑎 + 𝑑

𝑀3 = 𝑎 + 2𝑑 and so on where Mn = 𝑎 + (𝑛 − 1)𝑑

So, the terms are:

𝑎, 𝑎 + 𝑑 , 𝑎 + 2𝑑, 𝑎 + 3𝑑, 𝑎 + 4𝑑, 𝑎 + 5𝑑, 𝑎 + 6𝑑

Now, we can see that the sum of

Now, 𝑀2 + 𝑀4 + 𝑀6 = 𝑎 + 𝑑, 𝑎 + 3𝑑, 𝑎 + 5𝑑,

48 = 3𝑎 + 9𝑑 → 16 = 𝑎 + 3𝑑

Therefore,
𝑀1 + 𝑀3 + 𝑀5 + 𝑀7 = 𝑎 , 𝑎 + 2𝑑, 𝑎 + 4𝑑, 𝑎 + 6d

= 4𝑎 + 12𝑑
= 4(𝑎 + 3𝑑)
= 4 × 16
= 64

Here succeeding means eg: m1= m2-d . Am I right?

Yes correct. That is the translation of words into math

First translate the word equation given in the passage:
\(M2=M3-d\)
Notice that:
\(M3=M4-d\)
Which implies:
\(M2=M4-2d\)
From this we can derive a general pattern:
\(Mi=Mk-(k-i)d\)
For all k>i
We can rewrite the target statement then as:
\(M1+M1-2d+M1-4d+M1-6d\)
\(4M1-12d=?\)
We can also rewrite the given statement:
\(M2+M4+M6=48\)
\(M1-d+M1-3d+M1-5d=48\)
\(3M1-9D=48\)
\(M1-3D=16\)
\(4M1-12D=16*4=64\)
Giving us the solution to our target question, 64.