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# Let There Be an A.P. with the First Term 'A', Common Difference 'D'. If An A Denotes In Nth Term And Sn The Sum of First N Terms, Find. D, If a = 3, N = 8 and Sn = 192. - CBSE Class 10 - Mathematics

ConceptSum of First n Terms of an AP

#### Question

Let there be an A.P. with the first term 'a', common difference 'd'. If an a denotes in nth term and Sn the sum of first n terms, find.

d, if a = 3, n = 8 and Sn = 192.

#### Solution

Here, we have an A.P. whose first term (a), the sum of first n terms (Sn) and the number of terms (n) are given. We need to find the common difference (d).

Here,

First term (a) = 3

Sum of n terms (Sn) = 192

Number of terms (n) = 8

So here we will find the value of n using the formula, a_n = a + (a - 1)d

So, to find the common difference of this A.P., we use the following formula for the sum of n terms of an A.P

S_n = n/2 [2a + (n -1)d]

Where; a = first term for the given A.P.

d = common difference of the given A.P.

= number of terms

So, using the formula for n = 8, we get,

S_8 = 8/2 [2(3) + (8 - 1)(d)]

192 = 4[6 = (7) (d)]

192 = 24 + 28d

28d = 192 - 24

Further solving for d

d = 168/28

d= 6

Therefore, the common difference of the given A.P. is d = 6

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Solution Let There Be an A.P. with the First Term 'A', Common Difference 'D'. If An A Denotes In Nth Term And Sn The Sum of First N Terms, Find. D, If a = 3, N = 8 and Sn = 192. Concept: Sum of First n Terms of an AP.
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