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If the 7th and 14th terms of an A.P. are 34 and 62 respectively, what is the 20th term?
82
86
90
94
86
Notice the gap between terms: (14тИТ7)d=62тИТ34=28, so 7d=28, which implies d=4. To find the 20th term, add 6 steps of d to the 14th term: 62+(6├Ч4)=86.
7th term of the A.P. (a7тАЛ) = 34, 14th term of the A.P. (a1тАЛ4) = 62
anтАЛ=a+(nтИТ1)d
Notice the gap between terms: (14тИТ7)d=62тИТ34=28, so 7d=28, which implies d=4. To find the 20th term, add 6 steps of d to the 14th term: 62+(6├Ч4)=86.
Students often miscalculate the difference by setting it as 14dтИТ7d=62тИТ34 but accidentally solve for 7d incorrectly or use the wrong index for the target term.
Define the general term equation
The n-th term of an Arithmetic Progression is given by the formula anтАЛ=a+(nтИТ1)d. We write the equations for the 7th and 14th terms.
a+6d=34a+13d=62
Calculate common difference (d)
Subtract the first equation from the second equation to eliminate 'a' and solve for 'd'.
(a+13d)тИТ(a+6d)=62тИТ34тЯ╣7d=28тЯ╣d=4
Calculate the 20th term
We can express the 20th term using the 14th term: a20тАЛ=a14тАЛ+(20тИТ14)d. Substituting the known values a14тАЛ=62 and d=4.
a20тАЛ=62+6(4)=62+24=86
B is correct because the common difference is 4 and adding 6 increments to the 14th term results in 86.
This linear relationship (y=mx+c) is identical to the concept of slope in coordinate geometry, where d acts as the slope of the line passing through points (7,34) and (14,62).
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