Question

last test series 1, 2, 4,.....to 10 terms is​

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,.

⇒ $a_n = ar^{n-1}$

Here,

$r$ is the common ratio

$a_n$ is the nth term,

$a$ is the first term,.

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

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

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

Here, $S_n$ is the sum upto nth term,

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