The last term is (134), so \(d=\frac{134-18}{29}=4\). Exam tip: connect the average with the average of first and last terms.
Step 2
Why this answer is correct
The correct answer is A. (4). The last term is (134), so \(d=\frac{134-18}{29}=4\). Exam tip: connect the average with the average of first and last terms.
Step 3
Exam Tip
अंतिम पद (134) होगा इसलिए \(d=\frac{134-18}{29}=4\)। परीक्षा में औसत को प्रथम और अंतिम पद के औसत से जोड़ें।
The last term is (25+19(-2)=-13), so the average is \(\frac{25-13}{2}=6\). Exam tip: the average is the average of first and last terms.
Step 2
Why this answer is correct
The correct answer is B. (6). The last term is (25+19(-2)=-13), so the average is \(\frac{25-13}{2}=6\). Exam tip: the average is the average of first and last terms.
Step 3
Exam Tip
अंतिम पद (25+19(-2)=-13) है इसलिए औसत \(\frac{25-13}{2}=6\) है। परीक्षा में औसत प्रथम और अंतिम पद का औसत होता है।
The last term is (158), so \(d=\frac{158-2}{39}=4\). Exam tip: connect the average with the average of first and last terms.
Step 2
Why this answer is correct
The correct answer is D. (4). The last term is (158), so \(d=\frac{158-2}{39}=4\). Exam tip: connect the average with the average of first and last terms.
Step 3
Exam Tip
अंतिम पद (158) होगा इसलिए \(d=\frac{158-2}{39}=4\)। परीक्षा में औसत को प्रथम और अंतिम पद के औसत से जोड़ें।
Sum equals average \(\times\) number of terms, so \(64\times15=960\). If the average is given, the long formula is not necessary.
Step 2
Why this answer is correct
The correct answer is C. (960). Sum equals average \(\times\) number of terms, so \(64\times15=960\). If the average is given, the long formula is not necessary.
Step 3
Exam Tip
योग (=) औसत \(\times\) पदों की संख्या, इसलिए \(64\times15=960\)। औसत दिया हो तो लंबा सूत्र जरूरी नहीं है।
The twenty-third term is (104), so (S_{23}=\frac{23}{2}(16+104)=1380). With an odd number of terms, the middle term can also check the sum.
Step 2
Why this answer is correct
The correct answer is D. (1380). The twenty-third term is (104), so (S_{23}=\frac{23}{2}(16+104)=1380). With an odd number of terms, the middle term can also check the sum.
Step 3
Exam Tip
तेईसवाँ पद (104) है, इसलिए (S_{23}=\frac{23}{2}(16+104)=1380)। विषम पदों में मध्य पद से भी योग जाँचा जा सकता है।
The twenty-second term is (171), so (S_{22}=\frac{22}{2}(3+171)=1914). The average of the first and last terms is useful.
Step 2
Why this answer is correct
The correct answer is A. (1914). The twenty-second term is (171), so (S_{22}=\frac{22}{2}(3+171)=1914). The average of the first and last terms is useful.
Step 3
Exam Tip
बाईसवाँ पद (171) है, इसलिए (S_{22}=\frac{22}{2}(3+171)=1914)। पहले और अंतिम पद का औसत उपयोगी रहता है।
Sum equals average \(\times\) number of terms, so \(42\times11=462\). If the average is given, the long formula is not necessary.
Step 2
Why this answer is correct
The correct answer is B. (462). Sum equals average \(\times\) number of terms, so \(42\times11=462\). If the average is given, the long formula is not necessary.
Step 3
Exam Tip
योग (=) औसत \(\times\) पदों की संख्या, इसलिए \(42\times11=462\)। औसत दिया हो तो लंबा सूत्र जरूरी नहीं है।
The seventh term is (53), so (S_7=\frac{7}{2}(5+53)=203). With an odd number of terms, you can also check using the middle term.
Step 2
Why this answer is correct
The correct answer is A. (203). The seventh term is (53), so (S_7=\frac{7}{2}(5+53)=203). With an odd number of terms, you can also check using the middle term.
Step 3
Exam Tip
सातवाँ पद (53) है, इसलिए (S_7=\frac{7}{2}(5+53)=203)। विषम पदों में मध्य पद से भी जाँच सकते हैं।
Sum equals average \(\times\) number of terms, so \(27\times8=216\). If the average is given, the long formula is not needed.
Step 2
Why this answer is correct
The correct answer is B. (216). Sum equals average \(\times\) number of terms, so \(27\times8=216\). If the average is given, the long formula is not needed.
Step 3
Exam Tip
योग (=) औसत \(\times\) पदों की संख्या, इसलिए \(27\times8=216\)। औसत मिले तो लंबा सूत्र जरूरी नहीं।
The ninth term is (47), so (S_9=\frac{9}{2}(7+47)=243). With an odd number of terms, the middle term can also check the sum.
Step 2
Why this answer is correct
The correct answer is B. (243). The ninth term is (47), so (S_9=\frac{9}{2}(7+47)=243). With an odd number of terms, the middle term can also check the sum.
Step 3
Exam Tip
नौवाँ पद (47) है, इसलिए (S_9=\frac{9}{2}(7+47)=243)। विषम पदों में मध्य पद से भी योग जाँचा जा सकता है।
Sum equals average \(\times\) number of terms, so \(25\times9=225\). When the average is given, the long formula is not needed.
Step 2
Why this answer is correct
The correct answer is C. (225). Sum equals average \(\times\) number of terms, so \(25\times9=225\). When the average is given, the long formula is not needed.
Step 3
Exam Tip
योग (=) औसत \(\times\) पदों की संख्या, इसलिए \(25\times9=225\)। औसत दिए होने पर लंबा सूत्र जरूरी नहीं।
The first (6) terms go from (20) to (10), and the average is (15), so the sum is (90). The average of equally spaced terms is useful.
Step 2
Why this answer is correct
The correct answer is C. (90). The first (6) terms go from (20) to (10), and the average is (15), so the sum is (90). The average of equally spaced terms is useful.
Step 3
Exam Tip
पहले (6) पद (20) से (10) तक हैं और औसत (15) है, इसलिए योग (90) है। समान दूरी वाले पदों का औसत उपयोगी होता है।
The midpoint is \(\frac{\frac{5}{4}+\frac{9}{4}}{2}=\frac{7}{4}\). The average of two fractions gives the midpoint.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{7}{4}\). The midpoint is \(\frac{\frac{5}{4}+\frac{9}{4}}{2}=\frac{7}{4}\). The average of two fractions gives the midpoint.
Step 3
Exam Tip
मध्य बिंदु \(\frac{\frac{5}{4}+\frac{9}{4}}{2}=\frac{7}{4}\) है। दो भिन्नों का औसत मध्य बिंदु देता है।
