Question

a is an arithmetic sequence where the 1st term of the sequence is {\textstyle\frac{3}{2}} and the 13th term of the sequence is -{\textstyle\frac{81}{2}}. Find the 13th partial sum of the sequence.

Answer 1

195

Explanation:

a = 3/2

According to the formula tn= a + (n-1)d

81/2= 3/2 + (13 - 1)d

81/2= 3/2 + 12d

81/3 = 12d

Therefore 27/12 = d

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

`S_(13)` = 13/2 [2(3/2) + (13-1)(27/12)]

= 13/2 (3 + 27)

= 39/2 + 351/2

= 390/2

= 195