Question

last term of the series 1, 2, 4,.....to 10 terms in g.p

Answer 1

Answer:

Step-by-step explanation:

Given :

To find the 10th term & sum till 10 th term of the given series,.

1 , 2 , 4 ,...

Solution :

The given sequence is in G.P (Geometric Progression)

2⁰ = 0, 2¹ = 2 , 2² = 4 ,.. to 10th term,.

To find nth term of a gven G.P,.

⇒ a_n = ar^{n-1}a

n

=ar

n−1

Here,

rr is the common ratio

a_na

n

is the nth term,

aa is the first term,.

⇒ a_{10} = (1) \times (2)^{10 - 1} = 2^9 = 512a

10

=(1)×(2)

10−1

=2

9

=512

Sum of n terms in G.P is given by,

S_n = a[\frac{r^n - 1}{r-1}]S

n

=a[

r−1

r

n

−1

]

Here, S_nS

n

is the sum upto nth term,

⇒ S_{10}= 1[\frac{2^{10} - 1}{2-1} ]= \frac{1024-1}{1}= 1023S

10

=1[

2−1

2

10

−1

]=

1

1024−1

=1023

Answer 2

Step-by-step explanation:

20 is the correct answer hope it will be helpful