Question

If the sum of the sequence 1, 6, 11, 16 ........ x is 148, then find the value of x.

Plzz answer fast!! Class 10

Chapter : AP

No Class 9th students will answer this only 10th class people, answer fast!!

Answer 1

We have, AP 1,6,11,16,.............x 
a=1 and d = 5 

Let an = x
      a + (n-1)d = x
      1 + 5n-5 = x
     so, 5n - 4 = x
             n = x+4/5 .........................................(1)

We have, Sn = 148
                 n/2[a+an] = 148
                 n/2[1+x] = 148
        so, n[1+x] = 296
             By using (1)

           x+4/5[1+x] = 296
             [x+4](x+1) = 1480
       so, x²+5x+4 = 1480
           so, x²+5x - 1476 = 0 
    so, x² + 41x- 36x - 1476 = 0        [By splitting middle term]

    = x(x+41)   -36(x+41)
 so, x = 36,-41

But according to AP x couldn't be negative so, x = 36