Question

The sum of 3rd and 5th term of a.p is30and the sum of 4th and 8th term of ap issame 46 .find sum of first 10terms of ap

Answer 1

Answer:

210

Step-by-step explanation:

3rd term = a + 2d 5th term = a + 4d

3rd + 5th term = 30

a + 2d + a + 4d = 30

2a + 6d = 30

2(a + 3d) = 30

a + 3d = 30/2 = 15 (equ 1)

4th term = a + 3d = 15 8th term = a + 7d

4th + 8th = 46

15 + a + 7d = 46

a + 7d = 46 - 15 = 31 (equ 2)

equ 2 - 1

(a + 7d) - (a + 3d) = 31 - 15

4d = 16

d = 16/4 = 4

substitute d in equ 1

a + 3(4) = 15

a = 15 - 12

a = 3

sum of first 10 terms

S10 = n/2 (2a + (n-1)d)

$= \frac{10}{2} (2 \times 3 + (10 - 1)4) \\ = \frac{10}{2} (6 + 9(4)) \\ = 5 \times (6 + 36) \\ = 5 \times 42 \\ = 210$