Question

3) For a G.P., If a =2/3
and r = 3, then t6 =

A) 152
B) 162
C) 262
D) 252

​

Answer 1

ANSWER....

A) 152

THIS IS YOUR ANSWER PLS FOLLOW ME

Answer 2

Answer:

The value of $t_6$option (B), which is 162.

Explanation:

Given: In a Geometric Progression (G.P.),

           The value of the first term,

            $a=\frac{2}{3}$

           The common ratio,

            $r=3$

To find: The sixth term, $t_6$ .

Steps to be done while solving:

1. Write the given values.
2. Use the nth term of a G.P. formula.
3. Substitute the given values.
4. Simplify the expression.
5. Find the value of the required term.
6. Choose the correct option.

Formula to be used:

The nth term of a Geometric Progression can be found by the formula,

$t_n=ar^{n-1}$

Step 1 of 2:

From the given,

$a=\frac{2}{3} \\r=3\\n=6$

By substituting the above values in the formula, we get

$t_6=\frac{2}{3} (3^{6-1})$

Step 2 of 2:

By simplifying, we get

$t_6=\frac{2}{3} (3^5)\\=2(3^4)\\=2(81)\\=162$

Final answer:

Hence, the sixth term is 162.

Thus, option (B) is correct.