The first and last term of a linear sequence (AP) are 6 and 10 respectively. If the sum of the sequence is 40. Find the number of terms
A
nth = 3
B
nth = 4
C
nth = 5
D
nth = 6
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
nth term of a linear sequence (AP) = a+(n − 1)d
first term = 6, last term = 10 sum − 40
i.e. a = 6, l = 10, S = 40
\(S_n\)= n/2(2a + (n − 1)d or Sn = \div2 (a + l)
\(S_n\) = n/2(a + l)
40 = n/2(6 + 10)
40 = 8n
8n = 40
8n = 40
n = 40/8
= 5
The number of terms = 5
Source: Myschool Past Questions Archive (Record #40633)