Question

Consider an arithmetic sequence whose sum of first 9 terms is 261 and the sum of next 6 terms is 444
Find the first term and common difference and write the algebraic expression of the sequence

Answer 1

Answer:

a = 589, d = –61

Step-by-step explanation:

9 term

a+8d=261

6 term

a+5d=444

Answer 2

a = 17 , d = 6,

$a_{n} = 11 \: + 6n$

=

Step-by-step explanation:

Let the terms be a1 a2,a3,a4,a5,a6,a7,a8,a9, a10, a11,a12,a13,a14,a15

Sum of the first 6 terms = 9/2(2a1 + (9-1)d) = 261

(2a1 +8d) = 261×2/9

2a + 8d = 58...............(1)

Sum of the next six terms = 6/2(2a10 + (6-1)d) = 444

3(2( a1 + (10-1) d) + 5d) = 444

2a1 + 18d +5d = 148

2a1 + 23d = 148...............(2)

Subtracting 1 from 2

2a1- 2a1 + 23d -8d = 148-58

15d = 90

d= 90/15

d = 6

2a + 8 × 6 = 58

a + 4 ×3 = 29

a = 29-12 = 17

$a _{n} \: = a + (n - 1)d \\ = 17 + (n - 1)6 \\ a_{n} = 17 + 6n - 6 \\ = 11 + 6n$