Question

if the 7th term is 49 and 17th term is 289 in an AP find the first term and common difference​

Answer 1

$\huge\tt{\bold{\underline{\underline{Question᎓}}}}$If the 7th term is 49 and 17th term is 289 in an AP find the first term and common difference

$\huge\tt{\bold{\underline{\underline{Answer᎓}}}}$

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7th term of an A.P is 49 and 17th term is 289

Now solving separately,

Formulas:

$\bold{\boxed{an = a + (n - 1)d}}$

$a7 = a + 6d = 49$

$= > a = 49 - 6d.....(1)$

$a17 = a + 16d = 289$

Now, substitute a's value into equation

$= 49 - 6d + 16d = 289$

$= 49 + 10d = 289$

$= 10d = 240$

$\bold{\pink{ = > d = 24}}$

Now finding a's value

$a = 49 - 6d = 49 - 6 \times 24$

$\bold{\red{a= 49 - 144 = - 95}}$

Hence ,a=-95 & d=24

$\huge\mathcal{Other \:Formulas:}$

$\bold{\boxed{Sn = \frac{n}{2} (a + (n - 1) d}}$

when last term given

$\bold{\boxed{Sn = \frac{n}{2} (a + l)}}$

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