Question

How many terms of the ap:3,9,15,21,..........must be taken to given sum of 1875

Answer 1

Answer :

25 terms of Given AP will sum up 1875.

Given :

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

To find :

Number of terms of AP taken to give a sum 1875

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 1875

then,

→ Sₙ = (n/2) (2 a + (n-1) d)

→ 1875 = (n/2) [ 2(3) + (n-1) (6) ]

→ 1875 = (n/2) ( 6 + 6 n - 6 )

→ 1875 = (n/2) (6 n )

→ 1875 = 3 n²

→ n² = 1875 / 3

→ n² = 625

→ n = 25

Therefore,

25 terms of the given AP must be taken to give a sum of 1875.

Answer 2

Answer:

No. Of terms= 25

Step-by-step explanation:

n/2(2a + (n-1)d) = sum of ap

n/2(6 + (n-1)6) = 1875

n(6 + (n-1)6) = 3750

6n +6n² - 6n = 3750

n +n² - n = 625

n²= (25)²

n = 25

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