Question

how many terms of AP _6, _11/2, _5..... are
needed to give the sum _25​

Answer 1

Answer:

n=5,20. and a= -6 and d= 1/2

Answer 2

Answer:

No of terms = 5 ,20

Step-by-step explanation:

Given :

AP : -6, -11/2 , -5

To find:

No of terms to give sum = -25

Steps:

Firstly e calculate the common difference,

d = -11/2 -(-6)

  = -11/2 + 6

  = -1/2

Now, formula to calculate sum is:

Sn = n/2  (2a + (n-1)d)

$25 = \frac{n}{2}[2a+ (n-1)d]$

$25 = \frac{n}{2}[2*(-6)+ (n-1)*\frac{1}{2} ]\\\\25 = \frac{n}{2}[-12+ (n-1)\frac{1}{2} \\\\50 = -12n+ \frac{n^{2}-n }{2} \\\\100 = -24n+ n^{2}-n \\\\n^{2}-25n -100 = 0 \\\\(n-5)(n-20)=0\\\\n=5 , n=20$

#SPJ2