SELECT * FROM question_mgmt as q WHERE id=1064 AND status=1 SELECT id,question_no,question,chapter FROM question_mgmt as q WHERE courseId=2 AND subId=6 AND chapterId=80 and ex_no='5' AND status=1 ORDER BY CAST(question_no AS UNSIGNED) CBSE Free NCERT Solution of 11th mathematics Sequence and Series the sum of some terms of g p is 315 whose first t

Question:

The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

Answer:

Let the sum of n terms of the G.P. be 315.

It is known that, S subscript n space equals space fraction numerator a open parentheses r to the power of n space minus 1 close parentheses over denominator r minus 1 end fraction

It is given that the first term a is 5 and common ratio r is 2.

therefore space 315 space equals fraction numerator 5 open parentheses 2 to the power of n minus 1 close parentheses space over denominator 2 minus 1 end fraction rightwards double arrow 2 to the power of n space end exponent minus 1 space equals space 63 rightwards double arrow 2 to the power of n space equals 64 space equals space open parentheses 2 close parentheses to the power of 6 rightwards double arrow n equals 6

∴Last term of the G.P = 6th term = ar6 – 1 = (5)(2)5 = (5)(32) = 160

Thus, the last term of the G.P. is 160.


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