Question

Type the correct answer in each box,

Answer 1

Answer:

The $n^{th}$ sequence aₙ = -15 +5n

The fifth term of the sequence

a₅ = 10

Step-by-step explanation:

Step(i):-

Given sequence

           -10,-5,0,5,10,15,20,.....

The first term = -10

The difference of two terms in the given sequence is equal

d = -5-(-10) = -5 + 10 = 5

d = 0 -(-5) = 5

The given sequence is in arithmetic progression

Step(ii):-

The $n^{th}$ sequence

$a_{n} = a+(n-1) d$

aₙ = -10 +(n-1) 5

aₙ = -10 + 5n -5

aₙ = -15 +5n

Step(iii):-

The $n^{th}$ sequence aₙ = -15 +5n

put n = 5

a₅ = -15 + 5(5) = -15 +25 = 10

Final answer:-

The $n^{th}$ sequence aₙ = -15 +5n

The fifth term of the sequence

a₅ = 10