Question

write the first six terms of an A.P in which A=3.5,d=1.5​

Answer 1

Answer:

a = 3.5 , d = 1.5

a1 = a = 3.5

a2 = a+ d = 3.5 + 1.5 = 5

a3 = a+2d = 3.5 + 2(1.5) = 6.5

a4 = a + 3d = 3.5 + 3(1.5) = 8

a5 = a+4d = 3.5 + 4(1.5) = 9.5

a6 = a+5d = 3.5 + 5(1.5) = 11

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Answer 2

Answer:

The first six terms of the AP are 3.5, 5, 6.5, 8, 9.5, 11.

Step-by-step-explanation:

We have given that the first term of AP is 3.5 i. e. a = 3.5 and common difference is 1.5 i. e. d = 1.5.

We have to find first six terms of the AP.

$\sf\:t_{1}\:=\:a\:=\:3.5\\\\\sf\:t_{2}\:=\:t_{1}\:+\:d\:=\:3.5\:+\:1.5\:=\:5\\\\\sf\:t_{3}\:=\:t_{2}\:+\:d\:=\:5\:+\:1.5\:=\:6.5\\\\\sf\:t_{4}\:=\:t_{3}\:+\:d\:=\:6.5\:+\:1.5\:=\:8\\\\\sf\:t_{5}\:=\:t_{4}\:+\:d\:=\:8\:+\:1.5\:=\:9.5\\\\\sf\:t_{6}\:=\:t_{5}\:+\:d\:=\:9.5\:+\:1.5\:=\:11$

Additional Information:

1. Arithmetic Progression:

1. In a sequence, if the common difference between two consecutive terms is constant, then the sequence is called as Arithmetic Progression ( AP ).

2. $\sf\:n^{th}$ term of an AP:

The number of a term in the given AP is called as $\sf\:n^{th}$ term of an AP.

3. Formula for $\sf\:n^{th}$ term of an AP:

$\sf\:t_{n}\:=\:a\:+\:(\:n\:-\:1\:)\:d$

4. The sum of the first n terms of an AP:

The addition of either all the terms of a particular terms is called as sum of first n terms of AP.

5. Formula for sum of the first n terms of A. P. :

$\boxed{\red{\sf\:S_{n}\:=\:\frac{n}{2}\:[\:2a\:+\:(\:n\:-\:1\:)\:d\:]}}$