Question

Find:

(i) 10^th term of the A.P. 1, 4, 7, 10, ...

(ii) 18^th term of the A.P. $\sqrt{2},3\sqrt{2},5\sqrt{2}...$

(iii) n^th term of the A.P. 13, 8, 3, −2, ...

(iv) 10^th term of the A.P. −40, −15, 10, 35, ...

(v) 8th term of the A.P. 117, 104, 91, 78, ...

(vi) 11th term of the A.P. 10.0, 10.5, 11.0, 11.5, ...

(vii) 9th term of the A.P. $\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4},...$

Answer 1

In this problem, we are given different A.P. and we need to find the required term of that A.P.

(i) 10^th term of the A.P.

Here,

First term (a) = 1

Common difference of the A.P. (d)

Now, as we know,

So, for 10^th term,

Therefore, the 10^th term of the given A.P. is.

(ii) 18^th term of the A.P.

Here,

First term (a) =

Common difference of the A.P. (d)

Now, as we know,

So, for 18^th term,

Therefore, the 18^th term of the given A.P. is.

(iii) n^th term of the A.P.

Here,

First term (a) = 13

Common difference of the A.P. (d)

Now, as we know,

So, for n^th term,

Therefore, the n^th term of the given A.P. is.

(iv) 10^th term of the A.P.

Here,

First term (a) = -40

Common difference of the A.P. (d)

Now, as we know,

So, for 10^th term,

Therefore, the 10^th term of the given A.P. is.

(v) 8^th term of the A.P.

Here,

First term (a) = 117

Common difference of the A.P. (d)

Now, as we know,

So, for 8^th term,

Therefore, the 8^th term of the given A.P. is.

(vi) 11^th term of the A.P.

Here,

First term (a) = 10.0

Common difference of the A.P. (d)

Now, as we know,

So, for 11^th term,

Therefore, the 11^th term of the given A.P. is.

(vii) 9^th term of the A.P.

Here,

First term (a) =

Common difference of the A.P. (d)

Now, as we know,

So, for 9^th term,

Therefore, the 9^th term of the given A.P. is.