Question

If the 7th and 13th term of an arithmetic progression are 34 and 64 respectively yhen the common difference is

Answer 1

$7th \: term = \\ a + 6d = 34 \\ 13th \: term \\ a + 12d = 64 \\ subtract \\ 6d = 30 \\ d = 5$

Answer 2

Hey there !!


➡ Given :-

→ 7th term of AP ( $a \tiny 7$ ) = 34.

→ 13th term of AP ( $a \tiny 1$ ) = 64.


➡ To Find :-

→ The common difference (d).


➡ Solution :-

→ $a \tiny 7$ = 34.

=> a + ( n - 1 )d = 34.

=> a + ( 7 - 1 )d = 34.

=> a + 6d = 34........ (1).

And,

→ $a \tiny 13$ = 64.

=> a + ( n - 1 )d = 64.

=> a + ( 13 - 1 )d = 64.

=> a + 12d = 64........... (2).


▶ Substracte in equation (1) and (2), we get

a + 6d = 34.
a + 12d = 64.
(-)..(-)........(-).
__________

=> - 6d = - 30.

=> d = $\frac{ - 30 }{ - 6 } .$

$\huge \boxed{ \boxed{ \bf \therefore d = 5. }}$


✔✔ Hence, it is proved ✅✅.

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THANKS


#BeBrainly.