Question

if sum of first 6 terms of arithmetic progression is 117 and that of 12 terms is 486 find the sum of first 30 terms​

Answer 1

Answer:

3165

Step-by-step explanation:

Answer 2

The sum of first 30 terms of Arithmetic Progression is 3105

Step-by-step explanation:

Given data

Sum of first 6 terms of arithmetic progression $s_6 = 117$

Sum of first 12 terms of arithmetic progression $s_12 = 486$

To find - the sum of first 30 terms of arithmetic progression $s_(_3_0_)$

The formula to find the sum of first n terms of arithmetic progression is

$s_n = \frac{n}{2} ( 2a + (n- 1)d)$

Where n is the number of terms

a is the first term of the progression

d is the common difference

For the sum of first 6 terms,

$117 = \frac{6}{2} ( 2a + (6 - 1)d)$

$\frac{117}{3} = (2a + 5d)$

39 = 2 a +5 d -----> (1)

For the sum of first 12 terms ,

$486 = \frac{12}{2} ( 2a + (12 - 1)d)$

$486 = 6 ( 2a + 11d )$

$\frac{486}{6} = ( 2a + 11d )$

81 = ( 2 a + 11 d ) -----> (2)

Subtract (2) from (1)

we get, 6 d = 42

              d = 7

Substitute the value of 'd' in equation (2)

2 a + 11 (7) = 81

2 a + 77 = 81

2 a = 81 - 77

2 a = 4

a = 2

Then for the Sum of first 30 terms of arithmetic progression is

$s_3_0 = \frac{30}{2} [2 (2) + (30 - 1) (7)]$

$s_3_0 =15 [4 + (29) (7)]$

$s_3_0 =15 [4 + 203]$

$s_3_0 =15 [207]$

$s_3_0 = 3105$

Therefore the sum of first 30 terms of the arithmetic progression is 3105 when the sum of first 6 terms is 117 and sum of first 12 terms is 486.

To Learn More ...

1.  https://brainly.in/question/989035

2. https://brainly.in/question/1908665