Question

Number of terms of an AP : 9,17,25,... must be taken to give a sum 40500​

Answer 1

Answer:

Sn = 100

Step-by-step explanation:

First term = a = 9

Common difference = d = 8

sum of numbers formula

S = sum , n = number of terms

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

40500 = n/2 [2(9)+ (n-1)8]

40500 = n/2 ( 18+ 8n- 8 )

40500 = n/2 (10+8n)

40500 = n/2 × (10+8n)

40500 = n (5+4n)

40500 = 5n + 4n²

0 = 5n +4n² - 40500

(or)

4n² +5n -40500 = 0

split the middle term (5n)

4n²+405n -400n-40500 = 0

n (4n+405) -100 (4+405) = 0

(4n+405) (n-100) = 0

4n+ 405 = 0 and n- 100 = 0

n= - 405/4 and n = 100

n can't be a negative or fraction.

so n = 100

sum of 100 terms of this Ap = 40500

HOPE THIS ANSWER MAY HELPFULL