Question

In an AP 10th term is 21 and sum of first 10 term is 120 find the n the term of Arethametic progration


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Answer 1

Answer:

your answer in attachment

Answer 2

Solution

Given :-

• 10th terms of A.P. = 21
• Sum of 10th terms be = 120

Find :-

• nth terms of A.P.

Explantion

Using Formula

$\boxed{\tt{\red{\:(nth\:terms)\:=\:a+(n-1)d}}}$.

And,

$\boxed{\tt{\green{\:sum\:of\:nth\:terms\:=\:\dfrac{n[2a+(n-1)d]}{2}}}}$

Here,

• a = first terms
• n = Number of terms
• d = common Defference

So Now calculate 10th terms

Keep,

• n = 10

So,

==> 10th terms = a + (10-1)d

==> 21 = a + 9d ______________(1)

Again,

==> Sum of 10th terms = n{2a+(n-1)d}/2

==> 120 = 10{2a+(10-1)d}/2

==> 120 = 5{2a+(9d)}

==> 2a + 9d = 120/5

==> 2a + 9d = 24__________________(2)

Sub equ(1) & equ(2)

==> 2a - a = 24 - 21

==> a = 3

keep value of a in equ(1)

==> 21 = 3 + 9d

==> 9d = 21 - 3

==> 9d = 18

==> d = 18/9

==> d = 2

Since,

• First terms (a) = 3
• Common Defference (d) = 2.

______________________

For nth terms

==> nth terms = a + (n - 1)d

keep value of a & n

==> nth terms = 3 + (n-1)2

==> nth terms = 3 + 2n - 2

==> nth terms = 1 + 2n

Hence

• (1 + 2n) be required nth terms of A.P. series.

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