Question

The sum of the first and fifth term of an AP is 5, and of the twelve and sixteenth is 15. Find the sum of the first sixteen term

Answer 1

Answer:

a + a5 = 5 1.

a12 + a16 = 15 2.

Solving eq. 1.

a + a5 =5

a + a + 4d = 5

2a + 4d = 5

Solving eq. 2

a12 + a16 = 15

a + 11d + a +15d = 15

2a + 26d = 15

Subtracting 1 from 2

2a + 26d = 15

2a + 4d = 5

- - -

22d = 10

d = 10/22 = 5/11

Putting value of d in eq. 1

2a + 4d = 5

2a + 4×5/11 = 5

2a + 20/11 = 5

2a = 5 × 11/20

2a = 11/4

a = 11/4 ×1/2

a = 11/8

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

S16 = 16/2 [2×11/8 + (16-1) 5/11]

S16 = 8 ( 11/4 + 15 × 5/11)

S16 = 8 ( 11/4 + 75/11)

S16 = 8 (121 + 300/ 44)

S16 = 8 × 421/44

Then solve