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In an AP, if d = -4, n = 7 and a(n) = 4,...

In an AP, if d = -4, n = 7 and `a_(n)` = 4, then a is equal to

A

6

B

7

C

20

D

28

Text Solution

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The correct Answer is:
To find the value of \( a \) (the first term of the arithmetic progression), we can use the formula for the nth term of an arithmetic progression (AP): \[ a_n = a + (n - 1) \cdot d \] Where: - \( a_n \) is the nth term, - \( a \) is the first term, - \( n \) is the number of terms, - \( d \) is the common difference. Given: - \( d = -4 \) - \( n = 7 \) - \( a_n = 4 \) We can substitute the known values into the formula: \[ 4 = a + (7 - 1) \cdot (-4) \] Now, simplify the equation: 1. Calculate \( n - 1 \): \[ 7 - 1 = 6 \] 2. Substitute this value back into the equation: \[ 4 = a + 6 \cdot (-4) \] 3. Calculate \( 6 \cdot (-4) \): \[ 6 \cdot (-4) = -24 \] 4. Substitute this value back into the equation: \[ 4 = a - 24 \] 5. To isolate \( a \), add 24 to both sides: \[ 4 + 24 = a \] 6. Simplify the left side: \[ a = 28 \] Thus, the value of \( a \) is \( 28 \).
To find the value of \( a \) (the first term of the arithmetic progression), we can use the formula for the nth term of an arithmetic progression (AP): \[ a_n = a + (n - 1) \cdot d \] Where: - \( a_n \) is the nth term, ...
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