in an ap if a 18 - 13 is equal to 25 common difference is
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Class 10
>>Maths
>>Arithmetic Progressions
>>General Formula for nth Term
>>If the common difference of...
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If the common difference of an AP is 5, then what is a
18
−a
13
?
Medium
Solution
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Correct option is
C
25
Hint: n
th
term of an A.P. is a
n
=a+(n−1)d where a is first term and d is common difference.
Given:
value of common difference ,d=5
Step 1 : Find the value of 18
th
term i.e, a
18
by replacing n with 18 in the n
th
term of the A.P
⇒a
n
=a+(n−1)d
⇒a
18
=a+(18−1)d
∴a
18
=a+17d
Step 2 : Find the value of 13
th
term i.e, a
13
by replacing n with 13 in the n
th
term of the A.P
⇒a
n
=a+(n−1)d
⇒a
13
=a+(13−1)d
∴a
13
=a+12d
Step 3 : Find the difference between a
18
and a
13
a
18
−a
13
=[a+17d]−[a+12d]
=a+17d−a−12d
=5d
=5×5
=25
Final step : Hence, a
18
−a
13
=25
Step-by-step explanation:
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