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Let There Be an A.P. with the First Term ‘A’, Common Difference 'D’. If a Denotes Its Nth Term and Sn the Sum of First N Terms, Find. A, If An = 28, Sn = 144 and N= 9. - CBSE Class 10 - Mathematics

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Question

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

a, if an = 28, Sn = 144 and n= 9.

Solution

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

Here,

Last term (`a_9`) = 28

Sum of n terms (Sn) = 144

Number of terms (n) = 9

Now,

`a_9 = a + 8d`

28 = a + 8d   .....(1)

Also, using 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 = 9, we get,

`S_8 = 9/2 [2a + (9 -1 )(d)]`

144(2) = [2a + 8d]

288 = 18a + 72d ....(2)

Multiplying (1) by 9, we get

9a + 72d = 252 ....(3)

Further substracting (3) from (2) we get

9a = 36

`a = 36/9`

a = 4

Therefore, the first term of the given A.P. is a = 4

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Solution Let There Be an A.P. with the First Term ‘A’, Common Difference 'D’. If a Denotes Its Nth Term and Sn the Sum of First N Terms, Find. A, If An = 28, Sn = 144 and N= 9. Concept: Sum of First n Terms of an AP.
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