Question

Consider an arithmetic sequence where a1 = 5 and S9=297. find the common differece, d.

Answer 1

d = 7

The sum to n terms of an arithmetic sequence is

S
`_(n)` = n/2[ 2a₁ + (n - 1 )d]

here S₉ = 297

thus 9/2[ (2 × 5) + 8d] = 297

multiply both sides by 2 and divide by 9

10 + 8d = 66

subtract 10 from both sides

8d = 66 - 10 = 56

divide both sides by 8

d =
`(56)/(8)` = 7