Question

1. If tn =3n - 2, the value of S5 is:

(a) 35
(b) 40
(c) 45
(d) 30
If tn = 2n? + 3n, the value of Sais:
(a) 90
(b) 70
(C) 80
(d) None of these​

Answer 1

1) if tₙ = 3*n - 2, we want to find the value of S(5), which is the sum of the first 5 terms.

We can simply compute the sum directly, it is:

S(5) = t₁ + t₂ + t₃ + t₄ + t₅

S(5) = (3*1 - 2) + (3*2 - 2) + (3*3 - 2) + (3*4 - 2) + (3*5 - 2)

S(5) = 35

Then the correct option here is a).

2) This is not correctly written.

I will assume that we the n-th term is:

tₙ = n^2 + 3*n

And we want S(5) again

Then:

S(5) = t₁ + t₂ + t₃ + t₄ + t₅

S(5) = (1^2 + 3*1) + (2^2 + 3*2) + (3^2 + 3*3) + (4^2 + 3*4) + (5^2 + 3*5)

S(5) = 100

So the correct option is (d)

(Notice that if we had chosen any other S(n), the answer is still option (d) )