Question

how many terms are in the G.P 2,4,8,... upto 128​

Answer 1

Answer:

7 terms.

Step-by-step explanation:

Given:

First term a = 2

nth term Tn = 128

Common ratio r= 4/2 = 2

GP formula:

Tn = ar^(n-1)

So:

128 = 2 x 2^(n-1)

2^7 = 2^(1+n-1)

2^7 = 2^n

Comparing both sides.

7 = n

So there are 7 terms in the given GP.

Hope it helps.

Answer 2

There are 7 terms in the given G.P.

Given:

• A G.P.
• 2,4,8,..., 128

To find:

• Find the number of terms in given G.P.

Solution:

Formula/ Concept to be used:

1. General term of G.P.:$\bf a_n = a {r}^{n - 1}$where a is first term of G.P. and r is the common ratio.
2. $\bf {a}^{n}\times {a}^{m} = {a}^{n+m }$

Step 1:

Write the value of first term, common ratio ,and general term.

As G.P. is 2,4,8,...128

so,

$a = 2$

$r = 2$

and

$a_n = 128$

Step 2:

Put the values in the formula of general term.

$128 = 2 \times {2}^{n - 1}$

or

${2}^{7} = {2}^{1} \times {2}^{n - 1}$

or

${2}^{7} = {2}^{n - 1 + 1}$

or

${2}^{7} = {2}^{n }$

or

compare powers when base are same.

$\bf \red{n = 7}$

Thus,

There are 7 terms in the given G.P.

Learn more:

1) find five numbers in GP such that their sum is 31/4 and product is 1

https://brainly.in/question/18181027

2) The 4th and 7th and the last term of GP are 10 ,80 and 2560 is respectively find the first term and number of terms in G...

https://brainly.in/question/12926523