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The 7th and 21st terms of an AP are 6 and -22 respectively. Find the 26th term
Answer & Solution
Correct Answer:
Option
B
7th term = 6
21st term = -22
That means, 14 times common difference or -28 is added to 6 to get
-22
Thus, d = -2
7st term = 6 = a + 6d
Or, a + (6 × -2) = 6
Or, a = 18
26st term = a + 25d = 18 -25 × 2 = -32
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Logina7=6
a21=-22
Solution:-
a7=6
a+(7-1)d=6
a+6d=6..... . i
a21=-22
a+20d=-22.......ii
sub ii from i
a+6d-(a+20d)=6-(-22)
a+6d-a-20d=6+22
-14d=28
d=-2
putting value of d in equation i
a+6d=6
a+6×(-2)=6
a-12=6
a=6+12
a=18
now we have to find a26
a26=a+25d
a26=18+25×(-2)
a26=18-50
a26=-32
The 26th term is -32