Question

29. Find the 80th term of the arithmetic sequence -1, 1, 3, ....

Answer 1

In an Arithmetic Sequence the difference between one term and the next is a constant.

In general we could write an arithmetic sequence as-: {a, a+d, a+2d,........}

where:

• a is the first term, and
• d is the difference between the terms (called the "common difference")

In the given question, we have sequence as -: -1, 1, 3 ..............

so, here a = -1 (first term)

and d= (second term -first term) 1-(-1) = 2 = (third term - second term) = (3-1) = 2

Therefore, in this question d = 2 (common difference)

n^th term of an arithmetic sequence is given by: a_n = a+((n-1)*d)

Therefore, 80th term of above arithmetic sequence would be given by-:

a₈₀ = a+(80-1)*d = -1+(79*2) = 157

80th term of this arithmetic sequence is = 157