Q. 35.0( 5 Votes )

Find the eleventh

Answer :

We have the AP: 27, 23, 29, …, -65

Here, first term of the series (a) = 27


Common difference of the series (d) = 23 – 27 = -4


Last term of the series (an) = -65


We need to find position of -65, i.e., n.


We know the formula,


an = a + (n – 1)d


-65 = 27 + (n – 1)(-4)


-65 = 27 – 4n + 4


4n = 65 + 27 + 4


4n = 96




= 24


-65 is in the 24th position.


To find the eleventh term from the last term,


Position of the last term = 24th


Position of second last term = (24 – 1)th = 23rd


Position of third last term = (24 – 2)th = 22nd


Similarly, position of eleventh term from the last term = (24 – 10)th = 14th


11th term from the last term = 14th term from the beginning


Thus, taking n = 14, we need to find a14.


The formula of an = a + (n – 1)d


a14 = 27 + (14 – 1)(-4)


a14 = 27 – 52 = -25


Hence, the eleventh term from the last term of the AP is -25.

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