A.P series

$n^{\text{th}} \text{ term}= 17n - 10$ $({\color{#D61F06}{63}})^{\text{rd}} \text{ term}= 17({\color{#D61F06}{63}}) - 10$ $({\color{#D61F06}{63}})^{\text{rd}} \text{ term} = \boxed{1061}$

By observation,

$n^\text{th}$ term of the sequence $=17(n-1)+7$

Hence, $63^\text{rd}$ term of the sequence $=17(63-1)+7 = (17\times 62)+7 = 1054 +7 =\boxed{1061}$

It is an Arithmetic Progression with common difference, d = 17.

$a_{63} = a_1 + 62d = 7 + 62(17) = \boxed{1061}$

Since for and AP The difference of a term and it's preceding term is constant so

A2 -A1=A3 - A2=A4-A3 = d

So

A1 = a

A2 = a + d

A3 = a + d + d

A4 = a + d+ d+ d

. . .

. . .

. . .

. . .

An= a + (n-1)*d

So pu t n-63

And a= 7

And d= 17

We get - ans = 1061

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