Question

Time to Run Your BRAIN. REASONING QUESTION. Irreverent Answer = Report Appropriate Answer = BRAINLIEST

Answer 1

$\huge\bf\underline \green{ \mathcal{Q}uestion..}$

How many terms are in the sequence 1, 5 ,7 ,11,.....77?

$\large\bf\underline \blue {To \: \mathscr{f}ind:-}$

• we need to find the number of terms in the given AP.

$\huge\bf\underline \purple{ \mathcal{S}olution:-}$

$\bf\underline{\red{Given:-}}$

• Given AP = 1, 5, 7 , 11 ......77
• Last term = 77
• First term = 1

Common difference = a2 - a1

• a2 = 5
• a1 = 1

Common difference = 5 - 1

Common difference = 4

• ▶ we know that,

• $\bigstar \star \red{ \large \bold{a_n = a +(n - 1)d}}$

where,

• a = First term
• n = number of terms
• d = common difference
• an = last term

$\large \rightarrowtail \tt \: 77 = 1 + \bigg(n - 1 \bigg)4$

$\large\rightarrowtail \tt \: 77 = 1 + 4n - 4$

$\large\rightarrowtail \tt \: 77 = 4n - 3$

$\large\rightarrowtail \tt \: 77 + 3 = 4n$

$\large\rightarrowtail \tt \: 80 = 4n$

$\large\rightarrowtail \tt \: n = \cancel \frac{80}{4}$

$\large\rightarrowtail \bf \: n = 20$

Hence,

• There are 20 terms in the given sequence.

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