Question

In an arithmetic sequence u1=7, u20=64, un=3709 find the value of common difference and find the value of n

Answer 1

d = 3 and n = 1235

Explanation:

the nth term of an arithmetic sequence is

`u_(n)` = u₁ + d(n - 1)

where u₁ is the first term and d the common difference

given u₁ = 7 and u₂₀ = 64 , then

7 + 19d = 64 ( subtract 7 from both sides )

19d = 57 ( divide both sides by 19 )

d = 3

to find the number of terms n in the sequence.

Obtain the nth term formula and equate to 3709

`u_(n)` = 7 + 3(n - 1) = 7 + 3n - 3 = 3n + 4 ← nth term formula

3n + 4 = 3709 ( subtract 4 from both sides )

3n = 3705 ( divide both sides by 3 )

n = 1235