Question

the sum of first 5 terms of an ap is 55 the ratio of 8th term to 10th term is 13:16 calculate 6th term

Answer 1

Answer:

55=5/2(2a+4d)

110=5(2a+4d)

110=10a+20d

11=a+2d

a+7d/a+9d=13/16

16a+112d=13a+117d

3a=5d

Answer 2

Let a8 = 13 and a10 = 16

a10 = a8 + 2d

16 = 13 + 2d

2d = 3

d = 1.5

Sum = n/2 [2a + (n - 1) d] {a = 1st term

55 = 5/2 [2a + 4 × 1.5]

55 = 5/2 [2a + 6]

55 = 5a + 15

5a = 40

a = 8

a6 = a + 5d = 8 + 7.5

a6 = 15.5