Question

1. solve for x.

(I) 1+6+11+16+........+x=148

Answer 1

Hey buddy !!!

Apply AP .

Let , a = 1

d = a2 - a1

d = 6 - 1 = 5

common difference = 5

And sn = 148 ( given)

l = last term here x is last term

We know that ,

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

148 = n/2 ( 2× 1 + ( n - 1 )5

148 = n/2 ( 2 + 5n - 5 )

148 = n/2 ( 5n - 3 )

296 = n ( 5n - 3 )

296 = 5n² - 3n

5n² - 3n - 296 = 0

5n² - 40n + 37n - 296 = 0

5n ( n - 8 ) + 37 ( n - 8 ) =0

(5n + 37 ) ( n - 8 ) = 0

5n + 37 = 0

n = - 37/5 ( neglected)

Again ,

n - 8 = 0

n = 8

Here considerd n = 8

But , we wanna find out 'x' means last term of Ap

so , we know that next one formule


sn = n/2 ( a + l)

148 = 8/2 ( 1 + x)

148 = 4 + 4x

144 = 4x

x = 144/4 = 36

hence, ur answer is 36 ,

____________________________

Hope it helps you !!!

@Rajukumar111