Question

Plzx solve it with steps....

how many terms of the A P -6,11/2,-5......are needed to give the sum -25??




plzx give me all the steps....!!​

Answer 1

I think the second number is supposed to be negative, -11/2 = -5.5, because otherwise the sequence is not arithmetic.

The n-th term of the sequence, starting with n = 1, is then

-6 + 0.5 (n - 1) = 0.5n - 6.5

and we want to find the number N such that

`\displaystyle\sum_(n=1)^N(0.5n-6.5)=-25`

We have

`\displaystyle\sum_(n=1)^N(0.5n-6.5) = 0.5\sum_(n=1)^Nn-6.5\sum_(n=1)^N1\\ = 0.5*\frac{N(N+1)}2 - 6.5N \\= 0.25N^2-6.25N = -25`

Solve for N :

0.25 N ² - 6.25N + 25 = 0

N ² - 25N + 100 = 0

(N - 20) (N - 5) = 0

N = 20 or N = 5