An AP consists of 55 terms of which 5th term is 14 and last term is 144. Find the 29th term

29th term = 76.4

Step-by-step explanation:

Total terms = 55

aₙ = a + (n - 1) d

5th term = a₅ = 14

   a + (5 - 1)*d = 14

   a + 4d = 14  (I)

last term = a₅₅ = 144

               a + (55 - 1)d = 144

      a + 54d = 144(II)

Multiply equation (II) by (-1)

(I)             a +  4d = 14

(II)*(-1)     -a - 54d = -144  {Now add and thus a will be eliminated}

                   -50d = -130

 d = -130/-50

d = 2.6

Plug in d = 2.6 in equation (I)

a + 4* 2.6 = 14

  a  + 10.4 = 14

              a = 14 - 10.4

              a = 3.6

29th term = a₂₉ =  3.6 + (29 - 1)* 2.6

                          = 3.6 + 28* 2.6

                          = 3.6 + 72.8

                     a₂₉ =  76.4

76.4

Step-by-step explanation:

Let the first term and common difference of the AP be a and D respectively.

9514 1404 393

Step-by-step explanation:

The angle is in the 2nd quadrant, where the sine is positive and the cosine is negative.

tan^2(θ) +1 = sec^2(θ) = (-9/4)^2 +1 = 97/16   ⇒   sec = -(1/4)√97

cot(θ) = 1/tan(θ) = -4/9

csc^2(θ) = cot^2(θ) +1 = (-4/9)^2 +1 = 97/81   ⇒   csc = (1/9)√97

sin(θ) = 1/csc(θ) = (9√97)/97

cos(θ) = 1/sec(θ) = (-4√97)/97