Question

How many terms of an AP  - 6 , - 11/2, - 5 ..... are needed to give sum of -25 ?
1. 7
2. 18
3. 20
4. 8

Answer 1

Correct Answer - Option 3 : 20

Concept:

Let us consider sequence a1, a2, a3 …. an is an A.P.

• Common difference “d”= a2 – a1 = a3 – a2 = …. = an – an – 1

• nth term of the A.P. is given by an = a + (n – 1) d
• Sum of the first n terms = \(\rm S_n= \frac{n}{2}[2a+(n-1)\times d]\) = \(\rm\frac{n}{2}[a+l]\)

Where, a = First term, d = Common difference, n = number of terms, an = nth term and l = Last term

Calculation:

In the given question a = -6 and d = 1/2

S_n = - 25 

Here we use the formula S_n = \(\rm \frac{n}{2}\)[2a + (n - 1)d]

⇒ -25 = \(\rm \frac{n}{2}\)[2 × - 6 +(n - 1) × 1/2]

After solving this we get,

n² - 25n + 100 = 0

(n - 5) (n - 20) = 0

So n = 5 & 20