ICSE Class 10 Answered
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Asked by Kanwaranita10 | 03 Mar, 2020, 17:23: PM
If the 6th term of an AP is equal to four times its first term and the sum of first six terms is 75, find the first term and the common difference.
Solution:-
![G i v e n colon space a subscript 6 equals 4 a
rightwards double arrow a plus 5 d equals 4 a
rightwards double arrow 3 a minus 5 d equals 0 space... space left parenthesis i right parenthesis
S u m space o f space s i x space t e r m s space equals space 6 over 2 open parentheses 2 a plus open parentheses 6 minus 1 close parentheses d close parentheses
rightwards double arrow 3 open parentheses 2 a plus 5 d close parentheses equals 75
rightwards double arrow 2 a plus 5 d equals 25 space... space left parenthesis i i right parenthesis
A d d i n g space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis
rightwards double arrow 5 a equals 25 rightwards double arrow a equals 5
S u b s t i t u t i n g space a equals 5 space i n space left parenthesis i right parenthesis comma space w e space h a v e
3 cross times 5 equals 5 d space rightwards double arrow d equals 3](https://images.topperlearning.com/topper/tinymce/cache/2a89586a6922d80c5e5e06c9c6d0775e.png)
Answered by Renu Varma | 04 Mar, 2020, 10:14: AM
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