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If 23rd and 24th terms of an A.P. be 42 and 312 respectively, then its 37th term is:
3821
3820
3823
3822
3822
Calculate the common difference d directly as d = a2тАЛ4 - a2тАЛ3. Then, find the 37th term by adding (37-24) * d to the 24th term.
The 23rd term (a2тАЛ3) is 42 and the 24th term (a2тАЛ4) is 312 of an Arithmetic Progression.
anтАЛ=a+(nтИТ1)d
Calculate the common difference d directly as d = a2тАЛ4 - a2тАЛ3. Then, find the 37th term by adding (37-24) * d to the 24th term.
Students often miscalculate the common difference by subtracting the wrong way or miscounting the number of steps from the 24th to the 37th term.
Find the common difference
In an A.P., the common difference d is the difference between consecutive terms. So, d = a2тАЛ4 - a2тАЛ3.
d=312тИТ42=270
Use the formula for the nth term
To find the 37th term (a3тАЛ7) using the 24th term (a2тАЛ4), we use the relation: a3тАЛ7 = a2тАЛ4 + (37 - 24) * d.
a37тАЛ=a24тАЛ+13d
Calculate the 37th term
Substitute the values of a2тАЛ4 and d into the equation.
a37тАЛ=312+13├Ч270=312+3510=3822
D is correct because the calculated value of the 37th term is 3822.
This concept of linear growth is the foundation for Simple Interest calculations and Arithmetic Series, which are frequent topics in competitive exams.
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