Arithmetic Progression - For given arithemetic progression series 7,3,-1,-5,-9 ,... find 10 th term and addition of first 10 th terms. calculator

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Arithmetic Progression

1. For given arithemetic progression series 7,3,-1,-5,-9 ,... find 10 th term and addition of first 10 th terms.

Here first term

a=7, $a = 7,$

d=3-7=-4 $d = 3 - 7 = -4$

We know that,

f(n)=a+(n-1)d $f(n) = a + (n - 1)d$

f(10)=7+(10-1)(-4) $f(10) = 7 + (10 - 1)(-4)$

=7+(-36) $= 7 + (-36)$

=-29 $= -29$

We know that,

Sn=n2[2a+(n-1)d] $S_n = n/2 [2a + (n - 1)d]$

$:. S_10 = 10/2 * [2(7) + (10 - 1)(-4)]$

$= 5 * [14 + (-36)]$

$= 5 * [-22]$

$= -110$

Hence,

$10^(th)$ term of the given series is

$-29$ and sum of first

$10^(th)$ term is

$-110$