Question

The sum of the first 7 th term of an ap is 63 and the sum of its next 14 th term 161 find the 28th term of this ap

Answer 1

Step-by-step explanation:

sum of first 7 terms = 63

$63= \frac{n}{2} (2a + (n - 1)d) \\ 63 = \frac{7}{2} (2a + (7 - 1)d) \\ 63 = \frac{7}{2} (2a + 6d) \\ 63 = \frac{7}{2} \times 2(a + 3d) \\ \frac{63}{7} = a + 3d \\ a + 3d = 9$

a + 3d = 9 (4th term)

equ (1)

sum of next 14 terms = 161

8th term to 21st term

number of term is 14

first term will be = a + 7d

last term will be = a + 20d

$161 = \frac{14}{2} ((a + 7d) + (a + 20d)) \\ 161 = 7(2a + 27d) \\ \frac{161}{7} = 2a + 27d \\ 2a + 27d = 23$

equ (2) = 2a + 27d = 23

multiply equ (1) with 2

2a + 6d = 18 equ (3)

subtract (2) - (3)

2a + 27d - 2a - 6d = 23 - 18

21d = 5

d = 5/21

substitute d in equ 1

a + 3(5/21) = 9

a + 5/7 = 9

a = 9 - 5/7

a = 58/7

28th term = a + 27d

$= \frac{58}{7} + 27 \times \frac{5}{21} \\ = \frac{58}{7} + \frac{45}{7} \\ = \frac{103}{7}$

hope you get your answer