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Question
Q. First term is of arithmatic progression sequence is 48 and the difference between consecutive numbers is 13 , Find the sum numbers from 16 to 20 terms.
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Step : 1
Term at 16 position is 48 + (16 - 1)x 13
= [48 + (15)x 13 ]
= [48 + 195]
= [243]
ie. S16 = (243)
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Step : 2
Then,
Sum of 16 to 20 position is (5/2)[2*243 + (5 - 1)x 13 ]
= (2.5)[486 + (4)x 13]
= (2.5)[486 + 52]
= (2.5)[538]
ie. S16 to S20 = (1345)
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Step : 3
Second method:-
Term at 16 position is 48 + (16 - 1)x 13
= 243 (=t1)
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Step : 4
Term at 17 position is 48 + (17 - 1)x 13
= 256 (=t2)
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Step : 5
Term at 18 position is 48 + (18 - 1)x 13
= 269 (=t3)
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Step : 6
Term at 19 position is 48 + (19 - 1)x 13
= 282 (=t4)
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Step : 7
Term at 20 position is 48 + (20 - 1)x 13
= 295 (=t5)
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Step : 8
so the sequance of numbers from position 16 to 20 is 243, 256, 269, 282, 295
= 243 + 256 + 269 + 282 + 295
ie. S16 to S20 = 1345
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