An Ap is such that 5 th term is three times the 2nd term.given further that the sum of the 5th,6th,7th,8th term is240,calculate the value of the first term.

  5

Step-by-step explanation:

The general term of an arithmetic progression is ...

  an = a1 +d(n -1)

where a1 is the first term and d is the common difference.

Here we are given that ...

  a5 = 3×a2

  a5 +a6 +a7 +a8 = 240

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In terms of a1 and d, these tell us ...

  a1 +d(5 -1) = 3(a1 +d(2 -1))

  a1 +4d = 3a1 +3d . . . . . eliminate parentheses

  d = 2a1 . . . . . . . . . . . subtract a1+3d

and ...

  (a1 +4d) +(a1 +5d) +(a1 +6d) +(a1 +7d) = 240

  4a1 +22d = 240

Substituting for d, we have ...

  4a1 +22(2a1) = 240

  48a1 = 240

  a1 = 240/48 = 5

The first term is 5.

D. The volume will be 1/8 times the volume.

Step-by-step explanation:

We have been asked to find the affect on the volume of a pyramid if each side is multiplied by  factor of 1/2.

Let x and y be the sides of base of pyramid and z be the height of original pyramid.

Now each side of our pyramid is multiplied by a factor of 1/2, so sides of new pyramid will be:

,

,  

Let us substitute sides of new pyramid in volume formula to figure out volume of new pyramid.

We can see that volume of new pyramid is 1/8 times the volume of original pyramid, therefore, option D is the correct choice.