Question

The first and the last terms of an AP are 17 and 350 respectively. If the common difference
is 9 how many terms are there and what is their sum?
rotter of an AP in which d7 and 22nd term is 140​

Answer 1

—› Question :

The first and the last term of an AP are 17 and 350 respectively. If the common difference is 9. How many terms are there and what is their sum?

—› Given :

• $\tt \: First \: term (a) = 17$
• $\tt \: Last \: term (a_n) = 350$
• $\tt \: common \: difference (d) = 9$

—› To find :

• No. of term (n)
• Sum

—› Your Answer:

We know that,

$\implies \tt \: a_n = a + (n - 1)d \\ \implies \tt \: 350 = 17(n - 1)9 \\ \implies \tt \: 350 - 17 = 9n - 9 \\ \implies \tt \: 333 + 9 = 9n \\ \implies \tt \: 342 = 9n \\ \implies \tt \: \frac{ \cancel{342} \: ^{38} }{ \cancel9} = n \\ \\ \implies \tt \: n \: = 38$

Therefore,

No. of terms = 38 (ans)

Now,

$\implies \tt \: sum \: = \frac{n}{2} (2a + (n - 1)d)$

$\implies \tt \: sum \: = \frac{38}{2} (2 \times 17 + (38 - 1)9)$

$\implies \tt \: sum \: = \frac{ \cancel{38} \: ^{19} }{ \cancel2} (34 + 37 \times 9)$

$\implies \tt \: sum \: = 19(34 + 333)$

$\implies \tt \: sum \: = 19(367) \\ \\ \implies \tt \: sum \: =6973$

therefore,

sum = 6,973 (ans)