Method and examples
Arithmetic Progression
1. For given arithemetic progression series 7,3,-1,-5,-9 ,... find 10 th term and addition of first 10 th terms.
2. For arithemetic progression f( 5 ) = 56 , f( 8 ) = 86 then find f( 10 ) and S( 10 ).
3. For arithemetic progression f( 5 ) = 25 , f( 11 ) = 49 , then find n such that f(n) = 105 .
4. For arithemetic progression S( 33 ) = 198 , then find f( 17 ).
5. For arithemetic progression f( 17 ) = 6 , then find S( 33 ).
6. For arithemetic progression f( 7 ) = 13 , S( 14 ) = 203 , then find f( 10 ) and S( 8 ).
7. For arithemetic progression addition of 3 terms is 27 and their multiplication is 648 , then that numbers
8. For arithemetic progression addition of first 17 terms is 24 and addition of first 24 terms is 17 , then find addition of fir ...
9. For arithmetic progression Sm = n and Sn = m then prove that Sm+n = -(m - n)
10. For arithmetic progression Sm = n and Sn = m then prove that Sm-n = (m - n)(1 + 2n / m)
11. The ratio of two arithemetic progression series is 3x+5 : 4x-2 , then find the ratio of their 10 th term.
12. Find the sum of all natural numbers between 100 to 200 and which are divisible by 4 .
13. Find the sum of all natural numbers between 100 to 200 and which are not divisible by 4 .
14. For arithemetic progression addition of three terms is 15 and addition of their squres is 83 , then find that numbers
15. If S1, S2, S3 are sum of n, 2n, 3n terms of arithmetic progression series then prove that S3 = 3(S2 - S1)
16. If Sn is sum of n even terms of arithmetic progression series and Sn' is sum of n odd terms of arithmetic progression series ...
17. For arithemetic progression, addition of three terms is 51 and multiplication of end terms is 273 , then find that numbers
18. For arithemetic progression of four terms, addition of end terms is 14 and multiplication of middle two terms is 45 , then fi ...
19. For arithemetic progression, addition of four terms is 4 and addition of multiplication of end terms and multiplication of mi ...
Problem 8 of 19
8. For arithemetic progression addition of first terms is and addition of first terms is , then find addition of first terms.

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Arithmetic Progression
8. For arithemetic progression addition of first 17 terms is 24 and addition of first 24 terms is 17 , then find addition of first 41 terms. We know that, `S_n = n/2 [2a + (n - 1)d]` `S_17 = 17/2 * [2a + (17 - 1)d] = 24` `=> 17/2 * [2a + 16d] = 24` `=> 2a + 16 d = 2.8235 ->(1)` We know that, `S_n = n/2 [2a + (n - 1)d]` `S_24 = 24/2 * [2a + (24 - 1)d] = 17` `=> 24/2 * [a + 23d] = 17` `=> 2a + 23d = 1.4167 ->(2)` Solving `7 d = -1.4069` `=> d = -0.201` From `(1) => 2a + 16d = 2.8235` `=> 2a = 2.8235 - 16d` `=> 2a = 2.8235 - 16 × -0.201` `=> 2a = 2.8235 - -3.2157` `=> 2a = 6.0392` `=> a = 3.0196` We know that, `S_n = n/2 [2a + (n - 1)d]` `:. S_41 = 41/2 * [2(3.0196) + (41 - 1)(-0.201)]` `= 41/2 * [6.0392 + (-8.0392)]` `= 41/2 × -2` `= -41`