Question

the 4th term of ana AP is 11 and the 8th term exceed twice the 4th term by 5.find the AP and the sum of 1st of 50 term

Answer 1

a+3d = 11

a = 11-3d.....(1)

Again,

a+7d = 2(a+3d)+5

a+7d = 2a+6d + 5

a-2a+7d-6d = 5

-a + d = 5

Putting the Value of a in,

-a+d = 5

-(11-3d) + d = 5

-11+3d + d = 5

4d = 5+11

d = 16/4 = 4

Put the Value of D in (1)

a = 11-3d

a = 11-3×4= 11-12 = -1

AP = a , a+d , a+2d , a+3d ,......

Answer 2

[tex] a + 3d = 11\\ a + 7d =22 + 5 = 27 \\ 4d = 16\\d = 4\\ a = 11 -12= -1 \\ ap =-1,3,7,11........\\ s50 = \frac{50}{2} (2 \times -1+ (50 - 1) 4)\\ = 25( -2 + 196 ) \\ = 25 \times 194 = 4850