# Mathematics: Post your doubts here!

#### nathanseo

Excuse me . Do you have the <New syllabus Mathematics 7th > textbook1 with a compass on the face of the book. I need book1 textbook, please send me to "[email protected]"，thank you!!

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#### urmomm

my tiny braincells cant handle this!!
i need help with this Arithemetic progression question

#### Lemniscates

View attachment 71974
my tiny braincells cant handle this!!
i need help with this Arithemetic progression question
Given:-
[imath]a = 7[/imath]
[imath]t_n = 84[/imath]
[imath]t_{3n} = 245[/imath]

Formula to use:-
[imath]t_n = a + (n-1)d[/imath]

Solution:-

Form two equations with two pieces of information given in the question
[imath]7 + (n-1)d = 84[/imath]
[imath]7 + (3n-1)d = 245[/imath]

Now, we have two equations with two unknowns, we can solve them! Making d the subject and equating both equations:-
[imath]\rarr \frac{77}{n-1} = \frac{238}{3n-1}[/imath]
[imath]\rarr 77(3n-1) = 238(n-1)[/imath]
[imath]\rarr 231n - 77 = 238n - 238[/imath]
[imath]\rarr 7n = 161[/imath]

Hence,
[imath]\therefore n = 23[/imath]