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?​

Answer 1

Step-by-step explanation:

$\huge \red{Solution}$

Here,

a=17,tn=350,d=9

tn=a+(n-1)d...formula

350=17+(n-1)9

9(n-1)=350-17

9(n-1)=333

(n-1)=333/9

n-1=37

n=37+1

n=38

Sn=n/2[t1+tn]....formula

S38=38/2[17+350]

=19×367

S38=6973

There are 38 terms and their sum is 6973.

Hope it helps you

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Answer 2

$\large{ \dag{ \bold{ \red{ \underline{ \underline{Question...}}}}}}$

➭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?

$\large{ \dag{ \green{ \bold{ \underline{ \underline{Answer...}}}}}}$

$\large{ \sf{ n = 38 \: and \: s38 = 6973}}$

$\large{ \dag{ \red{ \bold{ \underline{ \underline{Solution...}}}}}}$

$\sf{ \star{ \purple{given....}}}$

• First term = 17
• Last term = 350
• Common Difference = 9

$\sf{ \star{ \purple{to \: find...}}}$

• No. of terms?
• Sum of all terms?

$\large{ \sf{ \to \: u \: must \: know....}} \\ \\ \large{ \orange{ \boxed{ \sf{ \red{a}n = a + (n - 1)d}}}} \\ \\ \sf{where \: a \: = \: first \: term} \\ \\ { \sf{\red{a}n = last \: term}} \\ \\ \sf{ n \: = \: no. \: of \: terms} \\ \\ \sf{d = common \: difference}$

$\large{ \sf {by \: using \:this \: formula...}} \\ \\ \large{ \sf{ \implies{350 = 17 + (n - 1)9}}} \\ \\ \large{ \sf{ \implies{333 = 9(n - 1)}}} \\ \\ \large{ \sf{ \implies{n - 1 = \cancel{ \frac{333}{9}} = 37}}} \\ \\ \large{ \sf{ \implies{n = 38}}} \\ \\ \large{ \purple{ \implies{ \boxed{no. \: of \: terms = 38}}}} \\ \\ \\ \large{ \sf{ \to \: \: sum \: of \: terms \: of \: ap\: formula}} \\ \\ \large{ \sf{ \orange{ \boxed{ \red{s}n = \frac{n}{2} 〚a + \red{a}n〛}}}} \\ \sf{ \red{s}n = sum \: of \: n \: terms} \\ \\ \\ \large{ \sf{by \: using \: this \: formula}} \\ \\ \large{ \sf{ \implies{s38 = \frac{38}{2} 〚17 + 350〛}}} \\ \\ \large{ \sf{ \implies{s38 \: = 19 \times 367}}} \\ \\ \large{ \sf{ \implies{ \purple{ \boxed{s38= 6973}}}}}$

$\large{ \bold{ \orange{ \underline{ \underline{required \: answer \: is \: n = 38 \: and \: sn = 6973}}}}}$