Question

Find the indicated terms in each of the following sequences whose nth terms are:

(a) a_n = 5n − 4; a₁₂ and a₁₅

(b) $a_n=\frac{3n-2}{4n+5};a_{7}and{a}_8$

(c) a_n = n (n −1) (n − 2); a₅ and a₈

(d) a_n = (n − 1) (2 − n) (3 + n); a₁, a₂, a₃

(e) a_n = (−1)ⁿ n ; a₃, a₅, a₈

Answer 1

Here, we are given the n^th term for various sequences. We need to find the indicated terms of the A.P.

(i)

We need to find and

Now, to find term we use, we get,

Also, to find term we use, we get,

$$\begin{gathered} a_{15}=5\left(15\right)-4 \\ =75-4 \\ =71 \end{gathered}$$

Thus,

(ii)

We need to find and

Now, to find term we use, we get,

Also, to find term we use, we get,

Thus,

(iii)

We need to find and

Now, to find term we use, we get,

Also, to find term we use, we get,

Thus,

(iv)

We need to find, and

Now, to find term we use, we get,

Also, to find term we use, we get,

Similarly, to find term we use, we get,

Thus,

(v)

We need to find, and

Now, to find term we use, we get,

Also, to find term we use, we get,

Similarly, to find term we use, we get,

Thus,