a+9d = -27
a+4d = -12
subtract:
5d = -15
d = -3
sub into a + 4d = -12 to find a, then use your definitions to find the rest of question.
btw, "..the sum of its 25th term" makes no sense
The 10th term of an ap is-27 and the 5th term is -12 what is the 18th find also the sum of its 25th term
2 answers
In AP n-th term is:
an = a + ( n - 1 ) d
where
a = first term
d = common difference
In this case:
a10 = a + 9 d
a10 = - 27
a + 9 d = - 27
a5 = a + 4 d
a5 = - 12
a + 4 d = - 12
Now you must solve system of two equations:
a + 9 d = - 27
a + 4 d = - 12
The solution is:
a = 0 , d = - 3
a18 = a + 17 d
a18 = 0 + 17 ∙ ( - 3 )
a18 = - 51
Sum of first n members of arithmetic progression is:
Sn = n [ 2 a + ( n - 1 ) d ] / 2
S25 = 25 ∙ [ 2 ∙ 0 + 24 ∙ ( - 3 ) ] / 2 = 25 ∙ ( 0 - 72 ) / 2 =
25 ∙ ( - 72 ) / 2 = - 1800 / 2
S25 = - 900
an = a + ( n - 1 ) d
where
a = first term
d = common difference
In this case:
a10 = a + 9 d
a10 = - 27
a + 9 d = - 27
a5 = a + 4 d
a5 = - 12
a + 4 d = - 12
Now you must solve system of two equations:
a + 9 d = - 27
a + 4 d = - 12
The solution is:
a = 0 , d = - 3
a18 = a + 17 d
a18 = 0 + 17 ∙ ( - 3 )
a18 = - 51
Sum of first n members of arithmetic progression is:
Sn = n [ 2 a + ( n - 1 ) d ] / 2
S25 = 25 ∙ [ 2 ∙ 0 + 24 ∙ ( - 3 ) ] / 2 = 25 ∙ ( 0 - 72 ) / 2 =
25 ∙ ( - 72 ) / 2 = - 1800 / 2
S25 = - 900
1 answer