Question

how many terms of an AP: 3,9,15,21,......... must be taken to give the sum 1452
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Answer 1

Answer :

22 terms of Given AP will sum up 1452

Step-by-step explanation:

Given :

AP : 3 , 9 , 15 , 21 .......

To find :

Number of terms of AP taken to give a sum 1452

Formulae required :

Sum of first n terms of AP with first term a common difference d  is given by

   Sₙ = (n/2) (2 a + (n-1) d)

Solution :-

we have,

▸first term of AP, a = 3

▸common difference of AP, d = 9 - 3 = 6

Let, n terms of given AP sum up to 1452

then,

→ Sₙ = (n/2) (2 a + (n-1) d)

→ 1452 = (n/2) [ 2(3) + (n-1) (6) ]

→ 1452 = (n/2) ( 6 + 6 n - 6 )

→ 1452 = (n/2) (6 n )

→ 1452 = 3 n²

→ n² = 1452 / 3

→ n² = 484

→ n = 22

Therefore,

22 terms of the given AP must be taken to give a sum of 1452.

HOPE THIS IS HELPFUL..