Question

Find the number of terms of the AP 18, `15``1/2` 13, ….., `49``1/2` and find the sum of all its terms n?

Answer 1

The AP is given as `18 , 15``1/2-18=-2``1/2`and the last term of the AP =`-49``1/2`

Let the AP has n terms.

∴a_n = a + (n − 1) d

`rArr -49``1/2=18-(n-1)xx2``1/2rArr-99/2=18-5/2(n-1)`

`rArr5(n-1)=135`

`thereforen=27+1=28`

Thus, the given AP has 28 terms.

Now, the sum of all the terms (S_n) is given by,

\[S_n = \frac{n}{2}\left[ 2a + \left( n - 1 \right)d \right] = \frac{28}{2}\left[ 2 \times 18 + \left( 28 - 1 \right) \times \left( - \frac{5}{2} \right) \right] = 14\left[ 36 - 27 \times \frac{5}{2} \right] = - 441\]

 

Thus, the sum of all the terms of the AP is -441.