Question

what is sum of first n terms of an arithametic sequence 4,12,20​

Answer 1

Answer:

Let the  first term be x

BTP

x/4=12/20

We know,  Product of extremes =Product of mean

20x=12×4

x=12×4/20

x=48/20

x=4.4

Here is your answer=4.4

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Answer 2

GIVEN:

• First term (a) = 4

TO FIND:

• What is the sum of n terms of an AP ?

SOLUTION:

We need to find the common difference of an AP

• d = a2–a1
• d = 12–4
• d = 8

First, we need to find the nth(l) term of an AP

❰ l = a + (n –1)d ❱

According to question:-

 ➛ l = 4 + (n –1)8

 ➛ l = 4 + 8n –8

 ➛ l = 8n –4

To find, the sum of n terms, we use the formula:-

❰ Sn = $\bf{\dfrac{n}{2}}$ [a + l] ❱

On putting the given values in the formula, we get

➛ Sn = $\sf{\dfrac{n}{2}}$ $\times$ [4 + 8n –4]

➛ Sn = $\sf{\dfrac{n}{2}}$ $\times$ 8n

➛ Sn = n $\times$ 4n

❮ Sn = 4n² ❯

❝ Hence, the sum of n terms is 4n² ❞

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