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

Solution:
Your problem `->` 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,`

`d = 3 - 7 = -4`

We know that, `f(n) = a + (n - 1)d`

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

`= 7 + (-36)`

`= -29`

We know that, `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`






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