Question

How many terms of the arithmetic sequence 5, 7, 9, ... must be added to get 140 ?

• A. 8
• B. 10
• C. 12
• D. 15

Answer 1

Answer:

B. 10

Sum of n terms = pn² + qn

p= half of the common difference

p+q = first term

common difference = 2

p=1

p+q = 5

q = 5-1

q=4

Sum = 140

$pn^2+qn=140$

$1n^2+4n=140$

$n^2+4n+4=140+4$

$(n+2)^2=144$

$n+2=\sqrt{144}$

$n+2=12$

$n=12-2=10$