Question

How many terms
terms of the AP -6,-11/2,-5___ are needed to give the sum – 25​

Answer 1

The value of "number of terms (n) is 5".

Step-by-step explanation:

The given sequence are - 6, - $\dfrac{11}{2}$, - 5, ......

Here, first term(a) = - 6 and

common difference (d) = - $\dfrac{11}{2}$ + 6 = $\dfrac{1}{2}$

Given, $S_{n}$ = - 25

We know that,

$S_{n}$ = $\dfrac{n}{2}$ ·{2a + ( n- 1)d}

⇒ $\dfrac{n}{2}$ ·{2( - 6) + ( n- 1) × $\dfrac{1}{2}$} = - 25

⇒ $\dfrac{n}{2}$ ·{ - 12 + $\dfrac{n}{2}$- $\dfrac{1}{2}$} = - 25

⇒ $n^{2}$ - 25n + 100 = 0

⇒ $n^{2}$ - 20n - 5n + 100 = 0

⇒ (n - 20)(n - 5) = 0

∴ n = 5 or 20 [∵ n = 20 is not satisfied]

n = 5

Hence, the value of "number of terms (n) is 5".