Question

12= 96 the sum of the A. P. 3, 7,11,.....is 210, the
number of terms
C) 15
22
62 12
a) 10​

Answer 1

Answer:

The answer is a option A

Answer 2

Answer:

Option A) 10 is the correct answer

The answer to this question briefly is given below:

Given things:

a=3                                    Sn=210

d= 7-3 =4                             n=?

$Sn= n/2[2a+(n-1)d]$

210= n/2[ 2 x 3+ (n-1)x 4]

210= n/2[ 6+4n-4]

210= n/2[2+4n]

210 x 2= 2n+ $4nx^{2}$

420= 2n+$4nx^{2}$

$4nx^{2}$+2n-420=0

By using quadratic formula:

a=4    b=2    c= -420

d= $bx^{2}$- 4ac

d= $2x^{2}$- 4 x 4 x-420

d= 4+6720

d= $6724\sqrt{x}$                   d=82

n= $-b+-\sqrt{x} bx^{2} -4ac$ ÷ $2a$

n= -2+-82÷ 2 x 4

n= -2+-82÷8

n= -2+82÷ 8                          n=-2-82÷8

n= 80÷8                                 n= -84÷8

n=10                                       n= 10.5

According to the no of terms, a decimal number cannot be included in AP

So that n=10

I hope this answer will be helpful to you