Find the partial sum Sn of the arithmetic sequence that satisfies the given conditions.

Question

a2 = 6, a5 = 7.5, n = 16?

Answer 1

Formula for the n^th term in arithmetic sequence = a +(n - 1)d

Second term in the arithmetic sequence = 6

a + d = 6 ---> (1)

Fifth term in the sequence a + 4d = 7.5 ---> (2)

Solve the equations (1) and (2).

From (1), d = - a + 6

Substitute a - 6 in equation (2).

a + 4(- a + 6) = 7.5

a - 4a + 24 = 7.5

- 3a + 24 = 7.5

- 3a = 7.5 - 24

a = - 16.5/-3

a = 5.5

Substitute a = 5.5 in equation (1).

5.5 + d = 6

d = 6 - 5.5

d = 0.5

Formula foe sum Sn = n/2 [ 2a + (n - 1)d]

Sn = 16/2 [2(5.5) + (16 - 1)(0.5)]

= 8 [11 + 7.5]

= 8[18.5]

Sum of 16 terms in the sequence = 148.