In an A.P., if the common difference d = - 3 and the eleventh term a_{11} = 15 , then find the first. term.
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In an A.P., if the common difference d = - 3 and the eleventh term a_{11} = 15 , then find the first. term.
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The value of the first terms of an A.P. is 45.
Step-by-step explanation:
Given:
The common difference d = - 3 of an A.P.
The eleventh term a_{11} =15
To Find:
The value of the first term of an A.P.
Formula Used:
nth term of an (A.P.), a_{n} = y+(n-1)d ---------------------- formula no.01.
Where
y = first term.
d= common difference.
n = number of the terms.
a_{n}= nth term of the Arithmetic Progression (A.P.).
Solution:
As given- The common difference d = - 3 of an A.P.
d= -3
As given-the eleventh term a_{11} =15
a_{11} =15 and n=15
Putting value of d, n and a_{11} in formula no.01.
[tex]15 = y+ (11-1)(-3)[/tex]
[tex]15 = y+ (10)(-3)[/tex]
[tex]15 = y- 30[/tex]
[tex]y=45[/tex]
Thus, the value of first term of an A.P. is 45.
We recall that, [tex]a_n[/tex] the term an A.P.
[tex]a_n=a+(n-1)d[/tex]
Given: [tex]d=-3, a_{11}=15[/tex]
[tex]15=a+(11-1)(-3)\\15=a+(10)(-3)\\15=a-30\\a=30+15\\a=45[/tex]
The first term of an A.P. is 45.