Q. 204.4( 7 Votes )

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Given: a11 : a18 = 2:3

To find: a5:a21

S5:S21

Formula Used:

Sum of “n” terms of an AP:

Where Sn is the sum of first n terms

nth term of an AP is:

an = a + (n - 1) d

Where an is the last term.

n = no of terms

a = first term

d = common difference

Explanation:

Let “a” and “d” the first term and common difference of an AP.

a11:a18 = 2:3

a + 10d : a + 17d = 2:3

3a + 30d = 2a + 34d

a = 4d [ eqn 1]

a5 = a + 4d = 4d + 4d = 8d [ by eqn 1] [ Eqn 2]

a21 = a + 20d = 4d + 20d = 24d [ by eqn 1] [ Eqn 3]

now using the formula

= 30d

= 21( 14 )d

= 294

S5:S21 = 30 : 294 = 5: 49

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