Sum
If the 8th term of an A.P is 37 and the 15th term is 15 more than the 12th term, find the A.P. Also, find the sum of first 20 terms of A.P.
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Solution
For an A.P
`t_8 = 37`
`=> a + 7d = 37` ....(i)
Also `t_15 - t_12 = 15`
`=> (a + 14d) - (a + 11d) = 15`
`=> a + 14d - a - 11d = 15`
=> 3d = 15
=> d= 5
Subsituting d = 5 in (i) we get
`a + 7 xx 5 = 37`
`=> a + 35 = 37`
=> a = 2
∴ Required A.P = a, a +d, a + 2d, a + 3d, .....
= 2, 7, 12, 17, .....
Sum of the first 20 terms of this A.P = `20/2 [2 xx 2 + 19 xx 5]`
= 10[4 + 95]
= 10 x 99
= 990
Concept: Arithmetic Progression - Finding Sum of Their First ‘N’ Terms.
Is there an error in this question or solution?
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