Question

If $n^th$ term of an A.P is represented by 4n - 15. Then find the sum of First 10 terms.

Answer 1

$\boxed{\boxed{\mathbf{70}}}$

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Given :

$n^{th}$ term of an A.P is represented by 4n - 15.

To Find :

Sum of First 20 terms.

$\underline{\underline{\huge\mathfrak{Solution :}}}$

let n = 1

Then,

$a_1$ = 4(1) - 15 = 4 - 15

$\boxed{\mathbf{a_1 = -11}}$

Similarly,

let n = 2

Then,

$a_2$ =  4(2) - 15 = 8 - 15[/tex]

$\boxed{\mathbf{a_2 = -7}}$

d = $\mathsf{a_2 - a_1 = -7 -(-11) = -7 + 11 }$

$\boxed{\boxed{\mathbf{d = 4}}}$

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So,

The A.P is

-11, -7, -3, 1, 5.....

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Now,

Using the Formula,

$\boxed{\large\mathbf{S_n = \frac{n}{2}(2a + (n-1)d)}}$

$\mathsf{=> \frac{10}{2}(2(-11) + (10-1)4)}$

$\mathsf{=> 5(-22 + 9(4))}$

$\mathsf{=> 5(-22 + 36)}$

$\mathsf{=> 5(14)}$

$\boxed{\mathbf{S_{10} = 70}}$

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