Question

If Tn=2n then sum of the first five terms is

Answer 1

Answer:

2,4,6,8,10

Step-by-step explanation:

Tn=2n

n is the term

if n = 1

T1 = 2(1) = 2 = 1st term

T2 = 2(2) = 4 = 2nd term

T3 = 2(3) = 6 = 3rd term

T4 = 2(4) = 8 = 4th term

T5 = 2(5) = 10 = 5th term

hence, first five terms are

2,4,6,8,10

Answer 2

Answer:

62

Step-by-step explanation:

We have given the generalised form of a G.P. as

$tn = {2}^{n}$

So, if we put,

$n = 1 \: \: then \: \bold{t1 = {2}^{1} = 2}$

$n = 2 \: \: then \: \bold{t2 = {2}^{2} = 4}$

$n = 3 \: \: then \: \bold{t3 = {2}^{3} = 8}$

$n = 4 \: \: then \: \bold{t4 = {2}^{4} = 16}$

$n = 5 \: \: then \: \bold{t5 = {2}^{5} = 32}$

So, we got our G.P. as,

2,4,8,16,32

Sum of these first 5 terms can be calculated in two ways,

Method I :

Add up directly,

$2 + 4 + 8 + 16 + 32 = 62$

Method II :

Use formula of 'Sum of n terms of a G.P.'

Here, a=2, n= 5 and r=2

So, we can use below formula,

$\boxed{Sn = \frac{a( {r}^{n} - 1)}{r - 1} }$

Substituting the values,

$Sn = \frac{2( {2}^{5} - 1) }{2 - 1}$

$Sn = \frac{2(32 - 1)}{1}$

$Sn = 2 \times 31$

$Sn = 62$