Question

a sequence of numbers is given by 25,30,35..............,300. find the number of terms in the sequence​

Answer 1

56

Explanation:

nth term = a+d(n-1) =25+5(n-1) = 25+5n-5 = 20+5n

300 = 20 + 5n

5n = 280

n = 56

since 300 is the last term in the sequence, the total number would be 36

Answer 2

56

Explanation:

clearly, the sequence is built by adding 5 for every new term.

so, an = an-1 + 5

a1 = 25 (the starting value)

a2 = a1 + 5 = 25 + 5 = 30

a3 = a2 + 5 = a1 + 5 + 5 = a1 + 2×5 = 25 + 10 = 35

...

an = an-1 + 5 = a1 + (n-1)×5

now, we know, the last term is 300.

when we determine for which n we get an = 300, we know that n is the number of terms in the sequence.

so,

300 = a1 + (n-1)×5 = 25 + 5n - 5 = 20 + 5n

280 = 5n

n = 56

a56 = 300

so, we have 56 terms in this sequence