Question

Find the sum of first 24 terms of the AP 5, 8 , 11, 14 ....​

Answer 1

Answer:

Given AP is 5, 8, 11, 14, ….. First term of given AP is a = 5. Common difference of given A.P is d = a2 – a1 = 8 – 5 = 3. We know that sum of first n terms of AP whose first term is a and common difference is d is given by Sn = n 2 n2 [2 + ( − 1)]. Therefore, the sum of first 24 terms of the given AP is S24 = 24 2 242 [2 × 5 + (24 − 1)3] = 12[10 + 23 × 3] = 12(10 + 69) = 12 × 79 = 948. (∵ a = 5, d = 3, n = 24)

• Hence, the sum of first 24 term of given AP is 948.

Answer 2

Answer

• The sum of first 24 terms of the AP = 948.

Given

• a = 5.
• d = 8 - 5 → 3.
• n = 24.

To Find

• The sum of first 24 terms of the AP.

Step By Step Explanation

Given :

• a = 5.
• d = 3.
• n = 24.

Formula Used :

$\red \bigstar \: \: \: \: \: \underline{\boxed{ \bold{ \purple{S_{n} = \cfrac{n}{2} \times \{2a + (n - 1)d \}}}}}$

By substituting the values :

Let's substitute the values in the above formula.

$\longmapsto \sf S_{n} = \cfrac{n}{2} \times \{2a + (n - 1)d \} \\ \\ \longmapsto \sf \cfrac{24}{2} \times \{2 \times 5 + (24 - 1) \times 3 \} \\ \\\longmapsto \sf \cfrac{24}{2} \times \{10+ 23 \times 3 \} \\ \\ \longmapsto \sf\cfrac{24}{2} \times \{10 + 69\} \\ \\ \longmapsto \sf\cfrac{ \cancel{24}}{ \cancel2} \times 79 \\ \\ \longmapsto \sf12 \times 79 \\ \\\longmapsto{ \underline{ \boxed{ \bold{ \green{ S_{n} = 948}}}}} \: \: \: \: \: \bigstar$

Therefore, the sum of first 24 terms of the AP = 948.

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