Question

write the sequence whose nth term is 31-n/3.find the sum of first 12 terms

Answer 1

If the sequence is an Arithmetic Progression with first term a and common difference d, then,

nth term = a + (n-1)d
⇒31-n/3 = a + nd -d
⇒31-n/3 = (a-d) +nd

Comparing the coefficients of n and the constants on both sides of the equation,

-1/3 = d
31=a-d
⇒a = 31+d = 31 - 1/3 =92/3

∴ The sequence is 92/3,91/3,90/3,...

Sum of n terms of an arithmetic progression is
(n/2)*(2a+(n-1)d)

∴Sum of 12 terms is

(12/2)*(2*92/3-(12-1)1/3)
=6*(184/3-11/3)
=6*173/3
=2*173
=346