Question

if for a GP r= 2 s10= 1023 find a​

Answer 1

welcome to the concept of gp

sum of n terms of gp

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

then ,

sum of 10 terms

$= a( \frac{2 {}^{10} - 1}{10 - 1} )$

given sum of 10 terms is 1023

then ,

$a = \frac{1023 \times 9}{2 {}^{10} - 1 }$

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Answer 2

Given,

For a GP,

r = 2

S10 = 1023

To find,

The value of a.

Solution,

The value of a will be 1.

We can easily solve this problem by following the given steps.

According to the question,

For a GP,

r = 2

S10 = 1023

We know that the sum of the n terms in a GP is given by the following formula:

Sn = $a(r ^n \: - 1) \div (r - 1)$

where r is greater than 1.

( a is the first term of the GP, n is the number of the term and r is the common ratio.)

$a(2 ^{10} - 1) \div (2 - 1)$ = 1023

a (1024-1)/1 = 1023

1023 × a = 1023

a = 1023/1023 (1023 was in the multiplication on the left-hand side. So, it is in the division on the right-hand side.)

a = 1

Hence, the value of a is 1.