Arithmetic progression
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This document defines an arithmetic progression as a sequence of numbers where each term is calculated by adding a fixed number (the common difference) to the preceding term. It provides the formulas to calculate the nth term and the sum of the first n terms of an arithmetic progression given the first term, common difference, and n. It also works through examples of finding the 12th term when the 1st term is 2 and common difference is 2, and finding the sum of the first 10 terms when the 1st term is 5 and common difference is 3.
Arithmetic progression
- 2. An A.P is a sequence of number in which each term is obtained by adding a fixed number to the preceding term except the 1st term. This fixed no is called the common difference{d},this number can be positive,negative or zero.
- 3. =d,where d=1 a a+d a+2d a+3d………………
- 4. an=a+(n-1)d where a is the 1st term d is the common difference an ,is a number which comes at the nth term.
- 5. Let a=2, d=2, n=12,find an? an=a+(n-1)d =2+(12-1)2 =2+(11)2 =2+22 Therefore, an=24 hence solved
- 6. c
- 7. S is the sum of 1st n terms. So, Sn=n/2{2a+(n-1)d} Sn=n/2{a+an} Sn=n/2{a+l},where l is the last term.
- 8. Let a=5, d=3, n=10, find Sn? We know that, Sn=n/2{2a+(n-1)d} =10/2{2(5)+(10-1)3} =5{10+9(3)} =5{10+27} =5{37} =185 Sn=185
- 10. CREDIT TO K.K SIR