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Paul [167]
3 years ago
13

(a) Find the common difference of an A.P. whose first term is 5 and the number of terms is 30 and sum 1455.

Mathematics
1 answer:
Alexxandr [17]3 years ago
4 0
Sum = n/2[2a + (n - 1)d] where a = first term, n = number of terms and d = common difference

(a) 30/2(2 x 5 + (30 - 1) x d) = 1455
10 + 29d = 1455 / 15
29d = 97 - 10
d = 87 / 29 = 3

(b) 7/2(2 x 9 + (7 - 1)d) = 0
18 + 6d = 0
6d = -18
d = -3
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There are 6 rotten mangoes and 24 good mangoes in a bag. What fraction of the mangoes is rotten?
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\sf \bf {\boxed {\mathbb {Given:}}}

Total number of rotten mangoes in the bag = 6

Total number of good mangoes in the bag = 24

\sf \bf {\boxed {\mathbb {To\:find:}}}

Fraction of the rotten mangoes to the total mangoes.

\sf \bf {\boxed {\mathbb {Solution:}}}

\implies {\blue {\boxed {\boxed {\purple {\sf { \frac{1}{5} }}}}}}

\sf \bf {\boxed {\mathbb {Step-by-step\:explanation :}}}

Total number of mangoes in the bag = Total number of rotten mangoes + Total number of good mangoes

➺\:6 + 24

➺\:30

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Fraction = \frac{Total \: \:   number  \:  \: of \:  \:  rotten \:  \:  mangoes}{Total  \:  \: number  \:  \: of \:  \:   mangoes}

➺\:  \frac{6}{30}

➺\:  \frac{1}{5}

Therefore, the fraction of the rotten mangoes to the total mangoes is \sf\pink{\frac{1}{5}}.

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