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

__

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.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

the answer is b