Question

Consider the arithmetic sequence 171, 167, 163,……….. 

(i) Is ‘0’ is a term of this sequence? Why? 

(ii) How many positive terms are in this sequence?

Answer 1

Arithmetic senes : 171, 167, 163 …………….

i. Here common difference

d = x₂ - x₁ = 167 - 171 = -4

Obtaining 0 as a term of this sequence 

0 - 171 = -171 is a multiple of common difference -4.

-171/-4 = 171/4

Quotient = 42, Remainder = 3

Remainder is not zero, so -171 is not a multiple of common difference -4.

∴ 0 will not be a term of the sequence

ii. Remainder = 3, ∴ 0 + 3 = 3 is a term of the sequence.

∴ 3 is the last positive term of the sequence.

∴ Sum of positive terms of the sequence

= \(\frac{x_n-x_1}{d}+1=\frac{3-171}{-4}+1\)

= (-168/-4) + 1 = 42 + 1 = 43