The sum of the first n terms of an a. p. is 2n and the sum of the first 2n terms is n. find the sum of the first 4n terms.

The sum of first 4n terms is -10n.

Step-by-step explanation:

The formula for sum of n terms of an AP is

It is given that the sum of the first n terms of an A. P. is 2n and the sum of the first 2n terms is n.

                         ..... (1)

                         ..... (2)

Solve equation (1) and (2) by elimination method.

The sum of first 4n terms is

Put the value of a and d.

Therefore the sum of 4n terms is -10n.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47