Question

If 1. a=3, d=-2, n=9 find an
2. f=-2, n=22, an=-39 find a
3. a=13, n=5, an=55 find d
4. a=12, d=4, an=56 find n​

Answer 1

Answer:

1. The nᵗʰ term of the AP is - 13.

2. The first term of AP i. e. a is 3.

3. The common difference ( d ) of the AP is 10.5.

4. The value of n of the AP is 12.

Step-by-step-explanation:

1.

We have given that,

• a = 3
• d = - 2
• n = 9

We have to find aₙ.

We know that,

aₙ = a + ( n - 1 ) × d - - [ Formula ]

→ a₉ = 3 + ( 9 - 1 ) × ( - 2 )

→ a₉ = 3 + 8 × ( - 2 )

→ a₉ = 3 - 16

→ a₉ = - 13

∴ The nᵗʰ term of the AP is - 13.

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2.

We have given that,

• d = - 2
• n = 22
• aₙ = - 39

We have to find the first term of AP i. e. a.

By using the formula, aₙ = a + ( n - 1 ) × d, we get,

→ - 39 = a + ( 22 - 1 ) × ( - 2 )

→ - 39 = a + 21 × ( - 2 )

→ - 39 = a - 42

→ a = - 39 + 42

→ a = 3

∴ The first term of AP i. e. a is 3.

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3.

We have given that,

• a = 13
• n = 5
• aₙ = 55

We have to find the common difference i. e. d.

By using the formula, aₙ = a + ( n - 1 ) × d, we get,

→ 55 = 13 + ( 5 - 1 ) × d

→ 55 = 13 + 4d

→ 55 - 13 = 4d

→ 4d = 42

→ d = 42 / 4

→ d = 10.5

∴ The common difference ( d ) of the AP is 10.5.

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4.

We have given that,

• a = 12
• d = 4
• aₙ = 56

By using the formula, aₙ = a + ( n - 1 ) × d, we get,

→ 56 = 12 + ( n - 1 ) × 4

→ 56 - 12 = ( n - 1 ) × 4

→ 44 = ( n - 1 ) × 4

→ ( n - 1 ) = 44 ÷ 4

→ n - 1 = 11

→ n = 11 + 1

→ n = 12

∴ The value of n of the AP is 12.